{"id":7362,"date":"2024-10-01T09:00:14","date_gmt":"2024-10-01T00:00:14","guid":{"rendered":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=7362"},"modified":"2025-09-30T17:02:31","modified_gmt":"2025-09-30T08:02:31","slug":"%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89","status":"publish","type":"post","link":"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/","title":{"rendered":"\u3010\u5b9f\u8df5\u7de8\u3011\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068ADMM\u306e\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u65b9\u5f0f\u306b\u3088\u308b\u4e0d\u7b49\u5f0f\u5236\u7d04\u3078\u306e\u5bfe\u51e6"},"content":{"rendered":"<p><a href=\"https:\/\/colab.research.google.com\/github\/T-QARD\/t-wave\/blob\/main\/notebooks\/QA_ADMM\/%E4%B8%8D%E7%AD%89%E5%BC%8F%E5%88%B6%E7%B4%84%E3%81%AB%E5%AF%BE%E3%81%99%E3%82%8BADMM.ipynb\" target=\"_blank\" rel=\"noopener noreferrer\"><img decoding=\"async\" src=\"https:\/\/colab.research.google.com\/assets\/colab-badge.svg\" alt=\"Open in Colab\"><\/a><\/p>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-white ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E6%89%8B%E6%B3%95\" >\u624b\u6cd5<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E6%8B%A1%E5%BC%B5%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5%E6%B3%95\" >\u62e1\u5f35\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u6cd5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E3%83%A1%E3%82%A4%E3%83%B3%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0\" >\u30e1\u30a4\u30f3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E5%AE%9F%E9%A8%93\" >\u5b9f\u9a13<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E6%BA%96%E5%82%99%EF%BC%9A%E5%90%84%E7%A8%AE%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB\" >\u6e96\u5099\uff1a\u5404\u7a2e\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A3%85\" >ADMM 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href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E6%9C%AC%E4%BD%93%E3%81%AE%E5%AE%9A%E7%BE%A9\" >ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u672c\u4f53\u306e\u5b9a\u7fa9<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E8%A7%A3%E3%81%8D%E3%81%9F%E3%81%84%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%EF%BC%88QKP%EF%BC%89%E3%81%AE%E5%AE%9A%E7%BE%A9\" >\u89e3\u304d\u305f\u3044\u6700\u9069\u5316\u554f\u984c\uff08QKP\uff09\u306e\u5b9a\u7fa9<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E6%80%A7%E8%83%BD%E8%A9%95%E4%BE%A1\" >ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u8a55\u4fa1<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Delta02_%E3%81%AE%E5%A0%B4%E5%90%88\" >$\\Delta=0.2$ \u306e\u5834\u5408<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C\" >ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97\" >Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83\" >\u7d50\u679c\u306e\u6bd4\u8f03<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Delta06_%E3%81%AE%E5%A0%B4%E5%90%88\" >$\\Delta=0.6$ \u306e\u5834\u5408<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C-2\" >ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97-2\" >Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83-2\" >\u7d50\u679c\u306e\u6bd4\u8f03<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Delta10_%E3%81%AE%E5%A0%B4%E5%90%88\" >$\\Delta=1.0$ \u306e\u5834\u5408<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C-3\" >ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97-3\" >Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83-3\" >\u7d50\u679c\u306e\u6bd4\u8f03<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E5%AE%9F%E9%A8%93%E7%B5%90%E6%9E%9C%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\" >\u5b9f\u9a13\u7d50\u679c\u306e\u307e\u3068\u3081<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E3%81%BE%E3%81%A8%E3%82%81\" >\u307e\u3068\u3081<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/2024\/10\/01\/%e3%80%90%e5%ae%9f%e8%b7%b5%e7%b7%a8%e3%80%91%e9%87%8f%e5%ad%90%e3%82%a2%e3%83%8b%e3%83%bc%e3%83%aa%e3%83%b3%e3%82%b0%e3%81%a8admm%e3%81%ae%e3%83%8f%e3%82%a4%e3%83%96%e3%83%aa%e3%83%83%e3%83%89\/#%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\" >\u3042\u3068\u304c\u304d<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%E6%A6%82%E8%A6%81\"><\/span><span style=\"font-size: 24px;\">\u6982\u8981<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u89e3\u8aac\u8a18\u4e8b\u300c<a href=\"\/T-Wave\/?p=5782\">\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068ADMM\u306e\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u65b9\u5f0f\u306b\u3088\u308b\u4e0d\u7b49\u5f0f\u5236\u7d04\u3078\u306e\u5bfe\u51e6<\/a>\u300d\u3067\u306f\u3001\u4e0d\u7b49\u5f0f\u5236\u7d04\u4ed8\u304d\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\uff08QA : Quantum Annealing\uff09\u3068 ADMM\uff08Alternating Direction Method of Multipliers\uff09\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u624b\u6cd5\u3092\u63d0\u6848\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u305d\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u3001\u5143\u8ad6\u6587\u306e\u518d\u73fe\u5b9f\u9a13\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E6%96%87%E7%8C%AE%E6%83%85%E5%A0%B1\"><\/span>\u6587\u732e\u60c5\u5831<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ul>\n<li>\u30bf\u30a4\u30c8\u30eb : Solving Inequality-Constrained Binary Optimization Problems on Quantum Annealer<\/li>\n<li>\u8457\u8005 : Kouki Yonaga, Masamichi J. Miyama, Masayuki Ohzeki<\/li>\n<li>\u66f8\u8a8c\u60c5\u5831 :<br \/>\n<a href=\"https:\/\/doi.org\/10.48550\/arXiv.2012.06119\">https:\/\/doi.org\/10.48550\/arXiv.2012.06119<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E6%89%8B%E6%B3%95\"><\/span>\u624b\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306f\u3058\u3081\u306b\u3001\u5143\u8ad6\u6587\u306b\u304a\u3044\u3066\u63d0\u6848\u3055\u308c\u305f\u624b\u6cd5\u3092\u7c21\u5358\u306b\u632f\u308a\u8fd4\u308a\u307e\u3059\uff08\u8a73\u7d30\u306f<a href=\"\/T-Wave\/?p=5782\">\u89e3\u8aac\u8a18\u4e8b<\/a>\u306b\u8a18\u8f09\u3057\u3066\u3044\u307e\u3059\uff09\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E6%8B%A1%E5%BC%B5%E3%83%A9%E3%82%B0%E3%83%A9%E3%83%B3%E3%82%B8%E3%83%A5%E6%B3%95\"><\/span>\u62e1\u5f35\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u6cd5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5143\u8ad6\u6587\uff08\u304a\u3088\u3073\u672c\u8a18\u4e8b\uff09\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u4e0d\u7b49\u5f0f\u5236\u7d04\u4ed8\u304d\u306e\u6700\u5c0f\u5316\u554f\u984c\u3092\u89e3\u304f\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$\\min_{\\pmb x} \\quad f ({\\pmb x}), \\quad {\\rm subject \\ to} \\quad {\\pmb G}_{m} {\\pmb x} \\le {D}_{m} \\quad (\\ m=1,\\cdots, M\\ )\\tag{1}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001$\\pmb x$ \u306f\u4e8c\u5024\u5909\u6570\u306e $N$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3001${\\pmb G}_{m}$ \u306f\u6574\u6570\u306e $N$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3001$D_{m}$ \u306f\u6574\u6570\u3067\u3059\u3002\u305d\u3057\u3066\u3001$f({\\pmb x})$ \u306f QUBO \u5f62\u5f0f\u3067\u5b9a\u7fa9\u3055\u308c\u308b\u76ee\u7684\u95a2\u6570\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (1) \u306e\u4e0d\u7b49\u5f0f\u5236\u7d04\u306f\u3001\u4ee5\u4e0b\u306e\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u3057\u3066\u8a18\u8ff0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u3053\u3053\u3067\u8a00\u3046\u30b3\u30b9\u30c8\u95a2\u6570\u3068\u306f\u3001\u5bfe\u8c61\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u6700\u5c0f\u5316\u3059\u308b\u95a2\u6570\u306e\u3053\u3068\u3067\u3059\uff09\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$E_{\\rm ineq} = f({\\pmb x}) + \\gamma \\sum_{m=1}^{M} \\Theta \\left( {\\pmb G}_{m} {\\pmb x} &#8211; D_{m} \\right) \\tag{2}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001$\\Theta$ $(x)$ \u306f\u30d8\u30f4\u30a3\u30b5\u30a4\u30c9\u306e\u30b9\u30c6\u30c3\u30d7\u95a2\u6570\u3067\u3001$x&gt;0$ \u306e\u3068\u304d\u306b $1$ \u3092\u53d6\u308a\u3001$x \\le 0$ \u306e\u3068\u304d\u306b $0$ \u3092\u53d6\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4efb\u610f\u306e $m$ \u306b\u3064\u3044\u3066$\\Theta ( {\\pmb G}_{m} {\\pmb x}^{\\ast} &#8211; D_{m} ) = 0 $ \u304c\u6210\u308a\u7acb\u3064\u3068\u304d ${\\pmb x}^{\\ast}$ \u306f\u5b9f\u884c\u53ef\u80fd\u89e3\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n<p>\u3057\u304b\u3057\u3001\u5f0f (2) \u306e $E_{\\rm{ineq}}$ \u306f\u30b9\u30c6\u30c3\u30d7\u95a2\u6570\u3092\u542b\u3093\u3067\u3044\u308b\u305f\u3081\u3001\u305d\u306e\u307e\u307e QUBO \u5f62\u5f0f\u306b\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\uff08\u3057\u305f\u304c\u3063\u3066\u3001D-Wave \u30de\u30b7\u30f3\u3067\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\uff09\u3002\u305d\u3053\u3067\u3001\u88dc\u52a9\u7684\u306a\u5909\u6570 $z_m$ \u3092\u5c0e\u5165\u3057\u3001 $E_{\\rm{ineq}}$ \u306e\u6700\u5c0f\u5316\u554f\u984c\u3092\u4e00\u65e6\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u66f8\u304d\u63db\u3048\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$\\min_{\\pmb x} \\quad f({\\pmb x}) + \\gamma \\sum_{m=1}^{M} \\Theta (z_m), \\quad {\\rm subject \\ to} \\quad {\\pmb G}_{m} {\\pmb x} &#8211; D_{m} = z_{m} \\ (\\ m=1,\\cdots, M\\ ) \\tag{3} $$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001$z_m$ \u306f\u6574\u6570\u306e $M$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002\u305d\u3057\u3066\u3001<br \/>\n\u5f0f (3) \u306b\u5bfe\u3057\u3066\u62e1\u5f35\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u6cd5\u3092\u9069\u7528\u3057\u3001\u65b0\u305f\u306a\u30b3\u30b9\u30c8\u95a2\u6570 $E_{\\rm{au}g}$ \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$E_{\\rm aug} ({\\pmb x}, {\\pmb z}, {\\pmb \\lambda}) = f({\\pmb x}) + \\gamma \\sum_{m=1}^{M} \\Theta (z_{m}) + \\sum_{m=1}^{M} \\lambda_{m} \\left( {\\pmb G}_{m} {\\pmb x} &#8211; D_m -z_m \\right) +\\frac{\\rho}{2} \\sum_{m=1}^{M} \\left( {\\pmb G}_{m} {\\pmb x}-D_m &#8211; z_m \\right)^2 \\quad \\tag{4}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001$\\lambda_m, \\rho$ \u306f\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u672a\u5b9a\u5b9a\u6570\u3067\u3059\u3002\u4ee5\u4e0b\u3067\u8aac\u660e\u3059\u308b ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u5f0f (4) \u306e $E_{\\rm{aug}}$ \u306e\u6700\u5c0f\u5316\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E3%83%A1%E3%82%A4%E3%83%B3%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0\"><\/span>\u30e1\u30a4\u30f3\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u305d\u308c\u3067\u306f\u3001\u5f0f (4) \u3092\u6700\u5c0f\u5316\u3059\u308b ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4ee5\u4e0b\u306b\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<ol>\n<li>\u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u521d\u671f\u5316\uff1a$\\{ z_m \\}=0, \\ \\{ \\lambda_m \\} = 0, \\ t=1$<\/li>\n<li>\u554f\u984c\u30b5\u30a4\u30ba $N$ \u306e\u5168\u7d50\u5408\u30b0\u30e9\u30d5\u3092 embedding \u3059\u308b<\/li>\n<li>\u5f8c\u8ff0\u3059\u308b\u5f0f (8) \u3092\u7528\u3044\u3066 QUBO \u884c\u5217\u3092\u8a08\u7b97\u3059\u308b<\/li>\n<li>QUBO \u884c\u5217\u3092\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3057\u3066\u30b5\u30f3\u30d7\u30eb $\\{ {\\pmb x}_{\\nu} \\}$ \u3092\u53d6\u5f97\u3059\u308b<\/li>\n<li>\u30b5\u30f3\u30d7\u30eb $\\{ {\\pmb x}_{\\nu} \\}$ \u304b\u3089 ${\\pmb x}_{\\rm cost}^{\\ast}$ \u3068 ${\\pmb x}_{\\rm feas}^{\\ast}$ \u3092\u8a08\u7b97\u3059\u308b<\/li>\n<li>$z_m^{\\ast}={\\rm min}(0, {\\pmb G}_{m} {\\pmb x}_{\\rm cost}^{\\ast}-D_{m}) \\ (\\ m=1,\\cdots, M\\ )$ \u306b\u3088\u308a $z_m^{\\ast}$ \u3092\u66f4\u65b0\u3059\u308b<\/li>\n<li>$\\lambda_{m} = \\lambda_{m} + \\rho\\ ({\\pmb G}_{m}{\\pmb x}_{\\rm cost}^{\\ast}-D_{m}-z_{m}^{\\ast})\\ (\\ m=1,\\cdots, M\\ )$ \u306b\u3088\u308a $\\lambda$ \u3092\u66f4\u65b0\u3059\u308b<\/li>\n<li>\u53ce\u675f\u306e\u78ba\u8a8d\uff1a\u4ee5\u4e0b\u306e\u6761\u4ef6\u306e\u3046\u3061\u4e00\u3064\u3067\u3082\u6e80\u305f\u3055\u308c\u305f\u3089\u8a08\u7b97\u3092\u7d42\u4e86\u3059\u308b\uff08\u6761\u4ef6\u5185\u306e\u30d1\u30e9\u30e1\u30fc\u30bf $t_{\\rm max}\\ , \\ t_{\\rm conv}\\ , \\ \\epsilon$ \u306f\u4e8b\u524d\u306b\u8a2d\u5b9a\u3059\u308b\uff09<\/li>\n<\/ol>\n<ul>\n<li>$t&gt;t_{\\rm{max}}$\uff08 \u6700\u5927\u30b9\u30c6\u30c3\u30d7\u6570 \uff09<\/li>\n<li>$E_{\\rm ineq} \\ ({\\pmb x}_{\\rm feas}^{\\ast}\\ )$ \u304c $t_{\\rm conv}$ \u30b9\u30c6\u30c3\u30d7\u306e\u9593\u6539\u5584\u3055\u308c\u306a\u3044<\/li>\n<li>$\\sqrt{\\sum_{m} ({\\pmb G}_{m} {\\pmb x}_{\\rm feas}^{\\ast} &#8211; D_m &#8211; z_m)^2 } &lt; \\epsilon$<\/li>\n<\/ul>\n<ol start=\"9\">\n<li>$t \\leftarrow t+1$<\/li>\n<li>\u624b\u9806 (3)~(10) \u3092\u53ce\u675f\u3059\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001${\\pmb x}_{\\rm{cost}}^{\\ast}$ \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$${\\pmb x}_{\\rm cost}^{\\ast}={\\rm argmin}_{\\{\\pmb x_{\\nu}\\}} \\quad E_{\\rm aug} \\ ({\\pmb x}, {\\pmb z}, {\\pmb \\lambda})\\tag{5}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3059\u306a\u308f\u3061\u3001\u30b5\u30f3\u30d7\u30eb $\\{ {\\pmb x}_{\\nu} \\}$ \u306e\u4e2d\u3067\u3001$E_{\\rm aug}$ $({\\pmb x}, {\\pmb z}, {\\pmb \\lambda})$ \u3092\u6700\u5c0f\u306b\u3059\u308b\u3082\u306e\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n<p>\u305d\u3057\u3066\u3001${\\pmb x}_{\\rm feas}^{\\ast}$ \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$${\\pmb x}_{\\rm feas}^{\\ast}={\\rm argmin}_{\\{ {\\pmb x}_{\\nu} \\}} \\quad f({\\pmb x}) \\quad {\\rm subject \\ to} \\quad {\\pmb G}_{m} {\\pmb x} \\le {\\pmb D}_{m} \\quad (m=1,\\cdots, M) \\tag{6}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3059\u306a\u308f\u3061\u3001\u30b5\u30f3\u30d7\u30eb $\\{ {\\pmb x}_{\\nu} \\}$ \u306e\u4e2d\u3067\u3001\u5168\u3066\u306e\u4e0d\u7b49\u5f0f\u5236\u7d04\u3092\u6e80\u305f\u3059\u3082\u306e\u306e\u3046\u3061\u3001$f({\\pmb x})$ \u3092\u6700\u5c0f\u306b\u3059\u308b\u89e3\u3092\u6307\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u5f8c\u306b\u51fa\u529b\u3059\u308b\u89e3\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93\"><\/span>\u5b9f\u9a13<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E6%BA%96%E5%82%99%EF%BC%9A%E5%90%84%E7%A8%AE%E3%83%A9%E3%82%A4%E3%83%96%E3%83%A9%E3%83%AA%E3%81%AE%E3%82%A4%E3%83%B3%E3%82%B9%E3%83%88%E3%83%BC%E3%83%AB\"><\/span>\u6e96\u5099\uff1a\u5404\u7a2e\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u307e\u305a\u306f\u3001\u5b9f\u88c5\u306b\u5fc5\u8981\u306a\u5404\u7a2e\u30e9\u30a4\u30d6\u30e9\u30ea\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>numpy\r\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>matplotlib\r\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>openjij\r\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>gurobipy\r\n<span class=\"o\">!<\/span>pip<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>-q<span class=\"w\"> <\/span>install<span class=\"w\"> <\/span>dwave-system\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"kn\">import<\/span> <span class=\"nn\">copy<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">math<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">random<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">statistics<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">mean<\/span><span class=\"p\">,<\/span> <span class=\"n\">stdev<\/span><span class=\"p\">,<\/span> <span class=\"n\">variance<\/span><span class=\"p\">,<\/span> <span class=\"n\">median<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">tqdm<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">trange<\/span>\r\n\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">numpy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">np<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.pyplot<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">plt<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">matplotlib.ticker<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">ticker<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">openjij<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">oj<\/span>\r\n<span class=\"kn\">import<\/span> <span class=\"nn\">gurobipy<\/span> <span class=\"k\">as<\/span> <span class=\"nn\">gp<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">gurobipy<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">GRB<\/span>\r\n<span class=\"kn\">from<\/span> <span class=\"nn\">dwave.system<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">DWaveCliqueSampler<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A3%85\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4><span class=\"ez-toc-section\" id=\"%E5%90%84%E7%A8%AE%E3%81%AE%E8%A3%9C%E5%8A%A9%E7%9A%84%E3%81%AA%E9%96%A2%E6%95%B0%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>\u5404\u7a2e\u306e\u88dc\u52a9\u7684\u306a\u95a2\u6570\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6b21\u306b\u3001ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e2d\u3067\u88dc\u52a9\u7684\u306b\u7528\u3044\u308b\u95a2\u6570\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306f\u3058\u3081\u306b\u3001\u5f0f (4) \u306e $E_{\\rm{aug}}$ \u304b\u3089 QUBO \u884c\u5217\u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570 compute_qubo_matrix \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u5f0f (4)\u3092 \u5c55\u958b\u3057\u3066\u5909\u6570 $\\pmb{x}$ \u304c\u542b\u307e\u308c\u308b\u9805\u3092\u6b8b\u3059\u3068\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$E_{\\rm aug}({\\pmb x}, {\\pmb z}, {\\pmb \\lambda})=f({\\pmb x})+\\sum_{m=1}^{M} \\lambda_{m}\\sum_{i=1}^{N}G_{m, i} x_i + \\frac{\\rho}{2}\\sum_{m=1}^{M} \\left( \\sum_{i=1}^{N} G_{m, i} x_{i} \\right)^2 &#8211; \\rho \\sum_{m=1}^{M} \\left( D_{m}+z_{m} \\right) \\sum_{i=1}^{N} G_{m, i} x_{i} \\tag{7}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u203b QA \u3067\u306f\u5909\u6570 ${\\pmb x}$ \u306b\u3064\u3044\u3066\u6700\u9069\u5316\u3059\u308b\u305f\u3081\u3001\u5909\u6570 ${\\pmb z}$ \u306e\u9805\u306f\u7121\u8996\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3055\u3089\u306b\u7b2c 3 \u9805\u306b\u3064\u3044\u3066\u5c55\u958b\u3057\u3001${\\pmb x}$ \u306b\u3064\u3044\u3066\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u6574\u7406\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$E_{\\rm aug} ({\\pmb x}, {\\pmb z}, {\\pmb \\lambda}) = f({\\pmb x}) + \\sum_{m=1}^{M} \\sum_{i=1}^{N} \\left\\{ \\lambda_{m} &#8211; \\rho \\left( D_{m}+z_{m} &#8211; \\frac{1}{2} G_{m,i} \\right) \\right\\} G_{m,i} x_{i} + \\rho \\sum_{m=1}^{M} \\sum_{i&lt;j} G_{m,i} G_{m,j} x_i x_j$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_qubo_matrix<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([[<\/span><span class=\"n\">f<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)])<\/span>  <span class=\"c1\"># \u307e\u305a f(x) \u306e\u4ee3\u5165<\/span>\r\n    <span class=\"c1\"># \u305d\u306e\u4ed6\u306e\u9805\u306e\u4ee3\u5165<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n            <span class=\"n\">Q<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">+=<\/span> <span class=\"p\">(<\/span><span class=\"n\">lam<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">rho<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"mf\">0.5<\/span> <span class=\"o\">*<\/span> <span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">]))<\/span> <span class=\"o\">*<\/span> <span class=\"n\">G<\/span><span class=\"p\">[<\/span>\r\n                <span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span>\r\n            <span class=\"p\">]<\/span>  <span class=\"c1\"># \u5bfe\u89d2\u9805<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n                <span class=\"n\">Q<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">rho<\/span> <span class=\"o\">*<\/span> <span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>  <span class=\"c1\"># \u975e\u5bfe\u89d2\u9805<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">Q<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u6b21\u306b\u3001\u4e0a\u306e compute_qubo_matrix \u95a2\u6570\u304b\u3089\u5f97\u3089\u308c\u305f QUBO \u884c\u5217\u3092 QA \u306b\u3088\u3063\u3066\u6700\u9069\u5316\u3059\u308b\u95a2\u6570 annealing_qubo_matrix \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">annealing_qubo_matrix<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">sampler<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># N_nu \u306f\u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n    <span class=\"n\">sampleset<\/span> <span class=\"o\">=<\/span> <span class=\"n\">sampler<\/span><span class=\"o\">.<\/span><span class=\"n\">sample_qubo<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">num_reads<\/span><span class=\"o\">=<\/span><span class=\"n\">N_nu<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">sampleset<\/span><span class=\"o\">.<\/span><span class=\"n\">record<\/span><span class=\"o\">.<\/span><span class=\"n\">sample<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7d9a\u3044\u3066\u3001\u30b5\u30f3\u30d7\u30eb ${\\pmb x}_{\\nu}$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u3001\u5f0f (7) \u306b\u57fa\u3065\u3044\u3066 $E_{\\rm aug}$ \u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570 compute_E_aug \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306f ${\\pmb x}_{\\rm cost}^{\\ast}$ \u3092\u6c42\u3081\u308b\u969b\u306b\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_E_aug<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">E_aug<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">),<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span>  <span class=\"c1\"># f(x) \u306e\u8a08\u7b97<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">Gx<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"p\">:],<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">E_aug<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">lam<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Gx<\/span> <span class=\"o\">+<\/span> <span class=\"n\">rho<\/span> <span class=\"o\">*<\/span> <span class=\"mf\">0.5<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"n\">Gx<\/span><span class=\"o\">**<\/span><span class=\"mi\">2<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"n\">rho<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">+<\/span> <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">])<\/span> <span class=\"o\">*<\/span> <span class=\"n\">Gx<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">E_aug<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (5) \u306b\u57fa\u3065\u3044\u3066 ${\\pmb x}_{\\rm cost}^{\\ast}$ \u3092\u6c42\u3081\u308b\u95a2\u6570 compute_x_cost \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u5185\u3067\u3001\u4e0a\u3067\u5b9a\u7fa9\u3057\u305f compute_E_aug \u95a2\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_x_cost<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u307e\u305a\u6700\u521d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u30b5\u30f3\u30d7\u30eb\u3092\u5165\u308c\u3066\u304a\u304f<\/span>\r\n    <span class=\"n\">E_temp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">compute_E_aug<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">x_cost<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x_nu<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"c1\"># \u4e8c\u756a\u76ee\u4ee5\u964d\u306e\u30b5\u30f3\u30d7\u30eb\u306b\u3064\u3044\u3066 E_aug \u3092\u6700\u5c0f\u306b\u3059\u308b\u3082\u306e (x_cost*) \u3092\u63a2\u7d22<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">nu<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">)):<\/span>\r\n        <span class=\"n\">E_aug<\/span> <span class=\"o\">=<\/span> <span class=\"n\">compute_E_aug<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">[<\/span><span class=\"n\">nu<\/span><span class=\"p\">],<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"n\">E_aug<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">E_temp<\/span><span class=\"p\">:<\/span>\r\n            <span class=\"n\">E_temp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">E_aug<\/span>\r\n            <span class=\"n\">x_cost<\/span> <span class=\"o\">=<\/span> <span class=\"n\">x_nu<\/span><span class=\"p\">[<\/span><span class=\"n\">nu<\/span><span class=\"p\">]<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">x_cost<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (6) \u306b\u57fa\u3065\u3044\u3066 $\\pmb{x}_{\\rm{feas}}^{\\ast}$ \u3092\u6c42\u3081\u308b\u95a2\u6570 compute_x_feas \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_x_feas<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">f_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n    <span class=\"n\">x_feas_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">x<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">x_nu<\/span><span class=\"p\">:<\/span>  <span class=\"c1\"># \u3059\u3079\u3066\u306e\u30b5\u30f3\u30d7\u30eb\u306b\u3064\u3044\u3066<\/span>\r\n        <span class=\"c1\"># \u3059\u3079\u3066\u306e m \u306b\u3064\u3044\u3066\u4e0d\u7b49\u5f0f\u6761\u4ef6\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u304b\u78ba\u8a8d<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"ow\">not<\/span> <span class=\"nb\">all<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"p\">:],<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)):<\/span>\r\n            <span class=\"k\">continue<\/span>\r\n\r\n        <span class=\"n\">f_temp<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># f(x) \u306e\u8a08\u7b97<\/span>\r\n        <span class=\"n\">f_list<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">f_temp<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">x_feas_list<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"k\">if<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas_list<\/span><span class=\"p\">)<\/span> <span class=\"o\">==<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>  <span class=\"c1\"># \u4e0d\u7b49\u5f0f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u30ea\u30b9\u30c8\u304c\u7121\u304b\u3063\u305f\u5834\u5408<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"p\">[]<\/span>\r\n    <span class=\"k\">else<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"n\">x_feas_list<\/span><span class=\"p\">[<\/span>\r\n            <span class=\"n\">f_list<\/span><span class=\"o\">.<\/span><span class=\"n\">index<\/span><span class=\"p\">(<\/span><span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"n\">f_list<\/span><span class=\"p\">))<\/span>\r\n        <span class=\"p\">]<\/span>  <span class=\"c1\"># x_feas_list \u306e\u4e2d\u3067\u3001f(x) \u3092\u6700\u5c0f\u306b\u3059\u308b\u3082\u306e (x_feas*) \u3092\u8fd4\u3059<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30b5\u30f3\u30d7\u30eb ${\\pmb x}_{\\nu}$ \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u306b\u3001\u5f0f (2) \u306b\u57fa\u3065\u3044\u3066 $E_{\\rm ineq}$ \u3092\u8a08\u7b97\u3059\u308b\u95a2\u6570 compute_E_ineq \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_E_ineq<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">gamma<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">E_ineq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">x<\/span><span class=\"p\">))<\/span>  <span class=\"c1\"># f(x) \u306e\u8a08\u7b97<\/span>\r\n\r\n    <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">f_step<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">int<\/span><span class=\"p\">(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"p\">:],<\/span> <span class=\"n\">x<\/span><span class=\"p\">)<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">])<\/span>  <span class=\"c1\"># \u30b9\u30c6\u30c3\u30d7\u95a2\u6570 Theta(G*x - D)<\/span>\r\n        <span class=\"n\">E_ineq<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">gamma<\/span> <span class=\"o\">*<\/span> <span class=\"n\">f_step<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">E_ineq<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u624b\u9806 8. \u3067 3 \u3064\u306e\u53ce\u675f\u6761\u4ef6\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u95a2\u6570 check_convergence \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u307e\u305f\u3001check_convergence \u95a2\u6570\u5185\u3067\u4f7f\u7528\u3059\u308b compute_criteria3 (\u53ce\u675f\u6761\u4ef6 3 \u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b\u95a2\u6570) \u3082\u4f75\u305b\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">compute_criteria3<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsilon<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">sum_c3<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">([(<\/span><span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"p\">:],<\/span> <span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span> <span class=\"o\">-<\/span> <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">])<\/span> <span class=\"o\">**<\/span> <span class=\"mi\">2<\/span> <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)])<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"p\">(<\/span>\r\n        <span class=\"n\">math<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">sum_c3<\/span><span class=\"p\">)<\/span> <span class=\"o\">&lt;<\/span> <span class=\"n\">epsilon<\/span>\r\n    <span class=\"p\">)<\/span>  <span class=\"c1\"># \u53ce\u675f\u6761\u4ef6 3 \u3092\u6e80\u305f\u3059\u5834\u5408\u306b\u306f True\u3001\u305d\u3046\u3067\u306a\u3051\u308c\u3070 False \u3092\u8fd4\u3059<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">check_convergence<\/span><span class=\"p\">(<\/span><span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">log<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"n\">t<\/span> <span class=\"o\">&gt;<\/span> <span class=\"n\">t_max<\/span><span class=\"p\">:<\/span>  <span class=\"c1\"># \u53ce\u675f\u6761\u4ef6 1 \u3092\u6e80\u305f\u3059\u5834\u5408<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"n\">log<\/span><span class=\"p\">:<\/span>\r\n            <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"condition : criteria 1 is satisfied.\"<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"kc\">True<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"p\">(<\/span>\r\n        <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq<\/span><span class=\"p\">)<\/span> <span class=\"o\">&gt;=<\/span> <span class=\"n\">t_conv<\/span> <span class=\"ow\">and<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"nb\">set<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq<\/span><span class=\"p\">[<\/span><span class=\"o\">-<\/span><span class=\"n\">t_conv<\/span><span class=\"p\">:]))<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"mi\">1<\/span>\r\n    <span class=\"p\">):<\/span>  <span class=\"c1\"># \u53ce\u675f\u6761\u4ef6 2 \u3092\u6e80\u305f\u3059\u5834\u5408<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"n\">log<\/span><span class=\"p\">:<\/span>\r\n            <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"condition : criteria 2 is satisfied.\"<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"kc\">True<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span> <span class=\"o\">!=<\/span> <span class=\"mi\">0<\/span> <span class=\"ow\">and<\/span> <span class=\"n\">compute_criteria3<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsilon<\/span>\r\n    <span class=\"p\">):<\/span>  <span class=\"c1\"># \u53ce\u675f\u6761\u4ef6 3 \u3092\u6e80\u305f\u3059\u5834\u5408<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"n\">log<\/span><span class=\"p\">:<\/span>\r\n            <span class=\"nb\">print<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"conditon : criteria 3 is satisfied.\"<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"k\">return<\/span> <span class=\"kc\">True<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"kc\">False<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E6%9C%AC%E4%BD%93%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u672c\u4f53\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u308c\u307e\u3067\u4f5c\u6210\u3057\u3066\u304d\u305f\u95a2\u6570\u3092\u7528\u3044\u3066 ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u672c\u4f53\u3092\u5b9a\u7fa9\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u624b\u9806 2. \u306b\u5bfe\u5fdc\u3059\u308b embedding \u3067\u306f DWaveCliqueSampler() \u3092\u7528\u3044\u308b\u3053\u3068\u3067\u5168\u7d50\u5408\u30b0\u30e9\u30d5\u3092\u57cb\u3081\u8fbc\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5168\u7d50\u5408\u30b0\u30e9\u30d5 \uff08clique\uff09 \u7528\u306b\u4e88\u3081\u7528\u610f\u3055\u308c\u305f\u57cb\u3081\u8fbc\u307f\u304c\u9069\u7528\u3055\u308c\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002\u307e\u305f\u3001\u4eca\u56de\u306f QA \u3068\u3057\u3066 D-Wave Advantage system6.3 \u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">qa_admm<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span> <span class=\"n\">gamma<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">E_ineq<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n    <span class=\"c1\"># \u624b\u9806 1 : \u30d1\u30e9\u30e1\u30fc\u30bf\u306e\u521d\u671f\u5316<\/span>\r\n    <span class=\"n\">z<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">lam<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">t<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>\r\n\r\n    <span class=\"c1\"># \u624b\u9806 2 : \u5168\u7d50\u5408\u30b0\u30e9\u30d5 (\u30b5\u30a4\u30ba N) \u306e embedding \u3092\u884c\u3046 ( = sampler \u306e\u6307\u5b9a)<\/span>\r\n    <span class=\"n\">dw_sampler<\/span> <span class=\"o\">=<\/span> <span class=\"n\">DWaveCliqueSampler<\/span><span class=\"p\">(<\/span><span class=\"n\">token<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"YOUR TOKEN\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">solver<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"Advantage_system6.3\"<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># SA \u306e\u5834\u5408 (\u57cb\u3081\u8fbc\u307f\u306f\u7121\u3057)<\/span>\r\n    <span class=\"c1\"># sa_sampler = oj.SASampler()<\/span>\r\n\r\n    <span class=\"k\">while<\/span> <span class=\"kc\">True<\/span><span class=\"p\">:<\/span>  <span class=\"c1\"># \u53ce\u675f\u6761\u4ef6\u3092\u6e80\u305f\u3059\u307e\u3067\u7e70\u308a\u8fd4\u3059<\/span>\r\n        <span class=\"c1\"># print(\"-\" * 50)<\/span>\r\n        <span class=\"c1\"># print(\"number of iterations = \", t)<\/span>\r\n\r\n        <span class=\"c1\"># \u624b\u9806 3 : QUBO \u884c\u5217\u3092\u8a08\u7b97\u3059\u308b<\/span>\r\n        <span class=\"n\">Q<\/span> <span class=\"o\">=<\/span> <span class=\"n\">compute_qubo_matrix<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">)<\/span>\r\n<span class=\"w\">        <\/span><span class=\"sd\">\"\"\"<\/span>\r\n<span class=\"sd\">        plt.imshow(Q)<\/span>\r\n<span class=\"sd\">        plt.colorbar()<\/span>\r\n<span class=\"sd\">        \"\"\"<\/span>\r\n        <span class=\"c1\"># \u624b\u9806 4 : QUBO \u884c\u5217\u3092\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3057\u3066\u30b5\u30f3\u30d7\u30eb\u3092\u53d6\u5f97<\/span>\r\n        <span class=\"n\">x_nu<\/span> <span class=\"o\">=<\/span> <span class=\"n\">annealing_qubo_matrix<\/span><span class=\"p\">(<\/span><span class=\"n\">Q<\/span><span class=\"p\">,<\/span> <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">dw_sampler<\/span><span class=\"p\">)<\/span>\r\n\r\n        <span class=\"c1\"># \u624b\u9806 5 : x_cost* \u3068 x_feas* \u3092\u8a08\u7b97\u3059\u308b<\/span>\r\n        <span class=\"n\">x_cost<\/span> <span class=\"o\">=<\/span> <span class=\"n\">compute_x_cost<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">lam<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">rho<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"c1\"># print(\"x_cost = \", x_cost)<\/span>\r\n        <span class=\"n\">x_feas<\/span> <span class=\"o\">=<\/span> <span class=\"n\">compute_x_feas<\/span><span class=\"p\">(<\/span><span class=\"n\">x_nu<\/span><span class=\"p\">,<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"c1\"># print(\"x_feas = \", x_feas)<\/span>\r\n\r\n        <span class=\"k\">for<\/span> <span class=\"n\">m<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">M<\/span><span class=\"p\">):<\/span>\r\n            <span class=\"n\">Gx_cost<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">dot<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">,<\/span> <span class=\"p\">:],<\/span> <span class=\"n\">x_cost<\/span><span class=\"p\">)<\/span>\r\n\r\n            <span class=\"c1\"># \u624b\u9806 6 : z \u3092\u30a2\u30c3\u30d7\u30c7\u30fc\u30c8\u3059\u308b<\/span>\r\n            <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">min<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">Gx_cost<\/span> <span class=\"o\">-<\/span> <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"c1\"># print(\"z[0] = \", z[m])<\/span>\r\n\r\n            <span class=\"c1\"># \u624b\u9806 7 : lambda \u3092\u30a2\u30c3\u30d7\u30c7\u30fc\u30c8\u3059\u308b<\/span>\r\n            <span class=\"n\">lam<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">+=<\/span> <span class=\"n\">rho<\/span> <span class=\"o\">*<\/span> <span class=\"p\">(<\/span><span class=\"n\">Gx_cost<\/span> <span class=\"o\">-<\/span> <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">z<\/span><span class=\"p\">[<\/span><span class=\"n\">m<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"c1\"># print(\"dot_Gmx_cost = \", Gx_cost)<\/span>\r\n            <span class=\"c1\"># print(\"dot_Gmx_cost-D[m]-z[m] = \", Gx_cost-D[m]-z[m])<\/span>\r\n            <span class=\"c1\"># print(\"lambda[0] = \", lam[m])<\/span>\r\n\r\n        <span class=\"c1\"># \u624b\u9806 8 : \u53ce\u675f\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\u3059\u308b<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span> <span class=\"o\">!=<\/span> <span class=\"mi\">0<\/span><span class=\"p\">:<\/span>\r\n            <span class=\"n\">E_ineq<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">compute_E_ineq<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">gamma<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">))<\/span>\r\n        <span class=\"c1\"># print(\"E_ineq = \", E_ineq)<\/span>\r\n        <span class=\"k\">if<\/span> <span class=\"n\">check_convergence<\/span><span class=\"p\">(<\/span>\r\n            <span class=\"n\">t<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span><span class=\"p\">,<\/span> <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span><span class=\"p\">,<\/span> <span class=\"n\">z<\/span><span class=\"p\">,<\/span> <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span> <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">log<\/span><span class=\"o\">=<\/span><span class=\"kc\">False<\/span>\r\n        <span class=\"p\">):<\/span>\r\n            <span class=\"k\">break<\/span>\r\n\r\n        <span class=\"c1\"># \u624b\u9806 9 : \u53cd\u5fa9\u56de\u6570 t \u3092\u66f4\u65b0\u3059\u308b<\/span>\r\n        <span class=\"n\">t<\/span> <span class=\"o\">+=<\/span> <span class=\"mi\">1<\/span>\r\n\r\n    <span class=\"k\">return<\/span> <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E8%A7%A3%E3%81%8D%E3%81%9F%E3%81%84%E6%9C%80%E9%81%A9%E5%8C%96%E5%95%8F%E9%A1%8C%EF%BC%88QKP%EF%BC%89%E3%81%AE%E5%AE%9A%E7%BE%A9\"><\/span>\u89e3\u304d\u305f\u3044\u6700\u9069\u5316\u554f\u984c\uff08QKP\uff09\u306e\u5b9a\u7fa9<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b9f\u88c5\u3057\u305f ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7cbe\u5ea6\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306b\u3001\u5143\u8ad6\u6587\u3068\u540c\u69d8\u306b\u4e8c\u6b21\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\uff08QKP : Quadratic Knapsack Problem\uff09\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059\u3002QKP \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$$\\max_{\\pmb x} \\quad {\\pmb x}^{\\top}P {\\pmb x},\\quad {\\rm subject \\quad to} \\quad {\\pmb w}^{\\top} {\\pmb x} \\le c \\tag{8}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (8) \u306b\u304a\u3044\u3066\u3001$x_i \\ (i=1,\\cdots, N)$ \u306f $i$ \u756a\u76ee\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\u6642\u306b $1$\u3001\u5165\u308c\u306a\u3044\u6642\u306b $0$ \u3092\u53d6\u308a\u307e\u3059\u3002$P= \\{ p_{i, j} \\}$ \u306f\u81ea\u7136\u6570\u304b\u3089\u306a\u308b $N\\times N$ \u306e\u884c\u5217\u3067\u3001$i$ \u756a\u76ee\u3068 $j$ \u756a\u76ee\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u305f\u3068\u304d\u306e\u4fa1\u5024\u3092\u8868\u3057\u307e\u3059\u3002$\\pmb{w}$ \u306f\u6b63\u306e\u6574\u6570\u306e $N$ \u6b21\u5143\u30d9\u30af\u30c8\u30eb\u3067\u3001\u5404\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u3092\u8868\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001$c$ \u306f\u5bb9\u91cf\uff08\u91cd\u91cf\u5236\u9650\uff09\u3092\u8868\u3059\u6b63\u306e\u6574\u6570\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b9f\u9a13\u3067\u306f\u3001$P$\u3001${\\pmb w}$\u3001${\\pmb x}$ \u3092\u30e9\u30f3\u30c0\u30e0\u306b\u751f\u6210\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u4fa1\u5024 $\\{ p_{i, j}\\}$ \u306f\u78ba\u7387 $(1-\\Delta)$ \u3067\u30bc\u30ed\u3001\u78ba\u7387 $\\Delta$ \u3067\u975e\u30bc\u30ed\u3068\u3057\u307e\u3059\u3002\u975e\u30bc\u30ed\u306e\u5024\u306f\u3001$1$ \u304b\u3089 $100$ \u306e\u4e00\u69d8\u5206\u5e03\u304b\u3089\u9078\u3073\u307e\u3059\u3002\u91cd\u91cf $w_i$ \u306b\u3064\u3044\u3066\u3082 $1$ \u304b\u3089 $50$ \u306e\u4e00\u69d8\u5206\u5e03\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3073\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u5bb9\u91cf $c$ \u306f $50$ \u304b\u3089 $\\sum_{i}w_i$ \u306e\u4e00\u69d8\u5206\u5e03\u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u3073\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5178\u578b\u7684\u306a\u6027\u80fd\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u306e\u30e9\u30f3\u30c0\u30e0\u306a QKP \u3092 10 \u500b\u751f\u6210\u3057\u307e\u3059\uff08\u3059\u306a\u308f\u3061\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6570 $N_{\\rm{inst}}=10$ \uff09\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u306a\u304a\u3001${\\pmb w}$ \u304a\u3088\u3073 $c$ \u306f\u305d\u308c\u305e\u308c\u5f0f (1) \u306e ${\\pmb G}_{m}$ \u304a\u3088\u3073 $D_m$ \u306b\u5bfe\u5fdc\u3057\u3001$\\max_{\\pmb x} \\ {\\pmb x}^{\\top} P {\\pmb x}$ \u306f $\\max_{\\pmb x} \\ f({\\pmb x})= &#8211; {\\pmb x}^{\\top}P {\\pmb x}$ \u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>\n<p>\u4ee5\u4e0b\u306b\u3001\u30e9\u30f3\u30c0\u30e0\u306a QKP \u3092\u751f\u6210\u3059\u308b\u95a2\u6570 make_QKP \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">make_QKP<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">Delta<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">f<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">G<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">))<\/span>\r\n    <span class=\"n\">D<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">((<\/span><span class=\"n\">M<\/span><span class=\"p\">))<\/span>\r\n\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">uniform<\/span><span class=\"p\">(<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"mi\">1<\/span><span class=\"p\">)<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">Delta<\/span><span class=\"p\">:<\/span>\r\n                <span class=\"n\">f<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"o\">-<\/span><span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">100<\/span><span class=\"p\">)<\/span>  <span class=\"c1\"># \u6700\u5927\u5316\u554f\u984c\u306a\u306e\u3067\u3001\u7b26\u53f7\u3092\u53cd\u8ee2\u3055\u305b\u308b<\/span>\r\n\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"mi\">50<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">D<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">random<\/span><span class=\"o\">.<\/span><span class=\"n\">randint<\/span><span class=\"p\">(<\/span><span class=\"mi\">50<\/span><span class=\"p\">,<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">[<\/span><span class=\"mi\">0<\/span><span class=\"p\">,<\/span> <span class=\"p\">:]))<\/span>\r\n\r\n    <span class=\"k\">return<\/span> <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E6%80%A7%E8%83%BD%E8%A9%95%E4%BE%A1\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u8a55\u4fa1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\Delta = 0.2, 0.6, 1.0$ \u306e\u5834\u5408\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u3001\u554f\u984c\u30b5\u30a4\u30ba $ N=8,16,32,64 $ \u306e QKP \u3092 10 \u500b\u305a\u3064\u751f\u6210\u3057\u3001ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u5404 QKP \u306b\u5bfe\u3059\u308b\u53b3\u5bc6\u89e3\u3092 Gurobi \u3067\u6c42\u3081\u3001ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u89e3\u3068\u6bd4\u8f03\u3057\u307e\u3059\u3002\u307e\u305a\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5404\u7a2e\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u8a2d\u5b9a\u3057\u3066\u304a\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">rho<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.1<\/span>\r\n<span class=\"n\">t_max<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">30<\/span>\r\n<span class=\"n\">t_conv<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">10<\/span>\r\n<span class=\"n\">epsilon<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">10<\/span> <span class=\"o\">**<\/span> <span class=\"p\">(<\/span><span class=\"o\">-<\/span><span class=\"mi\">3<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">gamma<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">100<\/span>\r\n<span class=\"n\">N_nu<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">2000<\/span>  <span class=\"c1\"># \u30b5\u30f3\u30d7\u30eb\u6570<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">10<\/span>  <span class=\"c1\"># \u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6570<\/span>\r\n<span class=\"n\">N_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">8<\/span><span class=\"p\">,<\/span> <span class=\"mi\">16<\/span><span class=\"p\">,<\/span> <span class=\"mi\">32<\/span><span class=\"p\">,<\/span> <span class=\"mi\">64<\/span><span class=\"p\">]<\/span>\r\n<span class=\"n\">len_N_list<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">N_list<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">M<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">1<\/span>  <span class=\"c1\"># \u4e0d\u7b49\u5f0f\u5236\u7d04\u306e\u6570\uff08\u5f0f(8)\u3088\u308a\uff11\u500b\uff09<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4><span class=\"ez-toc-section\" id=\"Delta02_%E3%81%AE%E5%A0%B4%E5%90%88\"><\/span>$\\Delta=0.2$ \u306e\u5834\u5408<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u554f\u984c\u30b5\u30a4\u30ba $ N=8,16,32,64 $ \u306e QKP \u3092\u30e9\u30f3\u30c0\u30e0\u306b 10 \u500b\u305a\u3064\u751f\u6210\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">Delta02<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.2<\/span>\r\n\r\n<span class=\"n\">f_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">G_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">D_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">N<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">N_list<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span> <span class=\"o\">=<\/span> <span class=\"n\">make_QKP<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">Delta02<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">f_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">G_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">D_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">D<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u751f\u6210\u3057\u305f QKP\uff08\u8a08 40 \u500b\uff09\u306b\u5bfe\u3057\u3066 ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_feas_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_ineq_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">qa_admm<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">f_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">G_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">D_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">rho<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">M<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_list<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span> <span class=\"o\">\/\/<\/span> <span class=\"n\">N_inst<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">gamma<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">x_feas_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_ineq_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [10:48&lt;00:00, 16.21s\/it]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97\"><\/span>Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u4eca\u5ea6\u306f\u305d\u308c\u305e\u308c\u306e QKP \u306b\u5bfe\u3057\u3066 Gurobi \u3092\u5b9f\u884c\u3057\u3001\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002\u307e\u305a\u306f Gurobi \u3067\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u308b\u95a2\u6570 grb_exact_qkp \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"k\">def<\/span> <span class=\"nf\">grb_exact_qkp<\/span><span class=\"p\">(<\/span><span class=\"n\">P<\/span><span class=\"p\">,<\/span> <span class=\"n\">w<\/span><span class=\"p\">,<\/span> <span class=\"n\">c<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">N<\/span> <span class=\"o\">=<\/span> <span class=\"nb\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">w<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"c1\"># \u554f\u984c\u3092\u8a2d\u5b9a<\/span>\r\n    <span class=\"n\">QKP<\/span> <span class=\"o\">=<\/span> <span class=\"n\">gp<\/span><span class=\"o\">.<\/span><span class=\"n\">Model<\/span><span class=\"p\">(<\/span><span class=\"n\">name<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"QKP\"<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u5909\u6570\u3092\u8a2d\u5b9a\uff08\u5909\u6570\u5358\u4f53\u306b\u304b\u304b\u308b\u5236\u7d04\u3092\u542b\u3080\uff09<\/span>\r\n    <span class=\"n\">x<\/span> <span class=\"o\">=<\/span> <span class=\"p\">{}<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">addVar<\/span><span class=\"p\">(<\/span><span class=\"n\">vtype<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"B\"<\/span><span class=\"p\">,<\/span> <span class=\"n\">name<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"x[<\/span><span class=\"si\">%x<\/span><span class=\"s2\">]\"<\/span> <span class=\"o\">%<\/span> <span class=\"n\">i<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u76ee\u7684\u95a2\u6570\u3092\u8a2d\u5b9a<\/span>\r\n    <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">setObjective<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">P<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">))<\/span> <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)),<\/span>\r\n        <span class=\"n\">GRB<\/span><span class=\"o\">.<\/span><span class=\"n\">MINIMIZE<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"c1\"># \u5236\u7d04\u3092\u8a2d\u5b9a<\/span>\r\n    <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">addConstr<\/span><span class=\"p\">(<\/span><span class=\"nb\">sum<\/span><span class=\"p\">(<\/span><span class=\"n\">w<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">*<\/span> <span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">))<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">c<\/span><span class=\"p\">,<\/span> <span class=\"n\">name<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"constraint\"<\/span><span class=\"p\">)<\/span>\r\n\r\n    <span class=\"c1\"># \u30ed\u30b0\u3092\u5207\u308b<\/span>\r\n    <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">params<\/span><span class=\"o\">.<\/span><span class=\"n\">LogToConsole<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">0<\/span>\r\n    <span class=\"c1\"># \u89e3\u3092\u6c42\u3081\u308b<\/span>\r\n    <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">optimize<\/span><span class=\"p\">()<\/span>\r\n    <span class=\"k\">if<\/span> <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">Status<\/span> <span class=\"o\">!=<\/span> <span class=\"n\">GRB<\/span><span class=\"o\">.<\/span><span class=\"n\">OPTIMAL<\/span><span class=\"p\">:<\/span>\r\n        <span class=\"k\">raise<\/span> <span class=\"ne\">Exception<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"\u6700\u9069\u89e3\u304c\u5f97\u3089\u308c\u307e\u305b\u3093\u3067\u3057\u305f\"<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"k\">return<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">array<\/span><span class=\"p\">([<\/span><span class=\"n\">x<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span><span class=\"o\">.<\/span><span class=\"n\">x<\/span> <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">)]),<\/span> <span class=\"n\">QKP<\/span><span class=\"o\">.<\/span><span class=\"n\">ObjVal<\/span>  <span class=\"c1\"># \u53b3\u5bc6\u89e3\u3068\u305d\u306e\u30b3\u30b9\u30c8\u3092\u8fd4\u3059<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u306e\u95a2\u6570\u3092\u7528\u3044\u3066\u3001\u5404 QKP \u306e\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_opt_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_opt_inst_D02<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">k<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_exact<\/span><span class=\"p\">,<\/span> <span class=\"n\">val_opt<\/span> <span class=\"o\">=<\/span> <span class=\"n\">grb_exact_qkp<\/span><span class=\"p\">(<\/span><span class=\"n\">f_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">],<\/span> <span class=\"n\">G_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">D_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span>\r\n    <span class=\"n\">x_opt_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_exact<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_opt_inst_D02<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">val_opt<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [00:01&lt;00:00, 25.96it\/s] \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83\"><\/span>\u7d50\u679c\u306e\u6bd4\u8f03<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u5f97\u3089\u308c\u305f\u89e3\u3068 Gurobi \u306e\u53b3\u5bc6\u89e3\u3068\u3092\u6bd4\u8f03\u3057\u307e\u3059\u3002\u53b3\u5bc6\u89e3\u3068\u6bd4\u8f03\u3057\u305f ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7cbe\u5ea6\u3092\u3053\u3053\u3067\u306f MAPE \u3067\u8a55\u4fa1\u3057\u307e\u3059\u3002MAPE \u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$${\\rm MAPE}=\\frac{1}{N_{\\rm inst}}\\sum_{k=1}^{N_{\\rm inst}} \\frac{| f_{k}({\\pmb x}_{\\rm opt}^{\\ast} \\ ) &#8211; f_{k}({\\pmb x}_{\\rm feas}^{\\ast}) |}{f_{k}({\\pmb x}_{\\rm opt}^{\\ast}\\ ) }\\tag{9}$$<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u3053\u3053\u3067\u3001$N_{\\rm inst}$ \u306f\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306e\u6570\uff08\u3057\u305f\u304c\u3063\u3066 $10$\uff09\u3001$f_k({\\pmb x}_{\\rm opt}^{\\ast})$ \u306f $k$ \u756a\u76ee\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u3064\u3044\u3066 Gurobi \u304b\u3089\u5f97\u305f\u6700\u9069\u89e3\uff08\u306b\u5bfe\u5fdc\u3059\u308b\u76ee\u7684\u95a2\u6570\uff09\u3001$f_k({\\pmb x}_{\\rm feas}^{\\ast})$ \u306f ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304b\u3089\u5f97\u305f\u6700\u9069\u89e3\uff08\u3003\uff09\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f(9)\u306b\u57fa\u3065\u304d\u3001\u554f\u984c\u30b5\u30a4\u30ba\u3054\u3068\u306b MAPE \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5e73\u5747\u304a\u3088\u3073\u6a19\u6e96\u8aa4\u5dee\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">mean_MAPE_D02<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">stder_MAPE_D02<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u6700\u9069\u5024\u306e\u7b26\u53f7\u3092\u53cd\u8ee2\u3055\u305b\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u6700\u5927\u5316\u554f\u984c\u306e\u6700\u9069\u5024\u306b\u623b\u3059<\/span>\r\n    <span class=\"n\">mean_MAPE_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">mean<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">stder_MAPE_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">stdev<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D02<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 4\/4 [00:00&lt;00:00, 1775.37it\/s]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b9f\u9a13\u7d50\u679c\u3068\u3057\u3066\u3001MAPE \u306e\u554f\u984c\u30b5\u30a4\u30ba $N$ \u4f9d\u5b58\u6027\u3092\u793a\u3059\u30b0\u30e9\u30d5\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">log2N_list<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[<\/span><span class=\"mi\">3<\/span><span class=\"p\">,<\/span> <span class=\"mi\">4<\/span><span class=\"p\">,<\/span> <span class=\"mi\">5<\/span><span class=\"p\">,<\/span> <span class=\"mi\">6<\/span><span class=\"p\">]<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">rcParams<\/span><span class=\"p\">[<\/span><span class=\"s2\">\"font.size\"<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"mi\">13<\/span>  <span class=\"c1\"># \u30d5\u30a9\u30f3\u30c8\u306e\u5927\u304d\u3055<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D02<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D02<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"o\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">xaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_major_locator<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">ticker<\/span><span class=\"o\">.<\/span><span class=\"n\">MaxNLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">integer<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>  <span class=\"c1\"># \u6a2a\u8ef8\u3092\u6574\u6570\u5024\u3067\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"MAPE\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$log_<\/span><span class=\"si\">{2}<\/span><span class=\"s2\">N$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$\\Delta=0.2$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" src=\"data:image\/png;base64,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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4><span class=\"ez-toc-section\" id=\"Delta06_%E3%81%AE%E5%A0%B4%E5%90%88\"><\/span>$\\Delta=0.6$ \u306e\u5834\u5408<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\Delta=0.2$ \u306e\u3068\u304d\u3068\u540c\u69d8\u306b\u3001\u554f\u984c\u30b5\u30a4\u30ba $ N=8,16,32,64 $ \u306e QKP \u3092\u30e9\u30f3\u30c0\u30e0\u306b 10 \u500b\u305a\u3064\u751f\u6210\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">Delta06<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">0.6<\/span>\r\n\r\n<span class=\"n\">f_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">G_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">D_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">N<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">N_list<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span> <span class=\"o\">=<\/span> <span class=\"n\">make_QKP<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">Delta06<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">f_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">G_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">D_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">D<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C-2\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u751f\u6210\u3057\u305f\u305d\u308c\u305e\u308c\u306e QKP \u306b\u5bfe\u3057\u3066 ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_feas_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_ineq_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">qa_admm<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">f_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">G_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">D_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">rho<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">M<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_list<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span> <span class=\"o\">\/\/<\/span> <span class=\"n\">N_inst<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">gamma<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">x_feas_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_ineq_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [15:08&lt;00:00, 22.71s\/it]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97-2\"><\/span>Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7d9a\u3044\u3066\u305d\u308c\u305e\u308c\u306e QKP \u306b\u5bfe\u3057\u3066 Gurobi \u3092\u5b9f\u884c\u3057\u3001\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_opt_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_opt_inst_D06<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">k<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_exact<\/span><span class=\"p\">,<\/span> <span class=\"n\">val_opt<\/span> <span class=\"o\">=<\/span> <span class=\"n\">grb_exact_qkp<\/span><span class=\"p\">(<\/span><span class=\"n\">f_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">],<\/span> <span class=\"n\">G_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">D_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span>\r\n    <span class=\"n\">x_opt_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_exact<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_opt_inst_D06<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">val_opt<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [00:07&lt;00:00,  5.66it\/s] \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83-2\"><\/span>\u7d50\u679c\u306e\u6bd4\u8f03<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (9) \u306b\u57fa\u3065\u304d\u3001\u554f\u984c\u30b5\u30a4\u30ba\u3054\u3068\u306b MAPE \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5e73\u5747\u304a\u3088\u3073\u6a19\u6e96\u504f\u5dee\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">mean_MAPE_D06<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">stder_MAPE_D06<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u6700\u9069\u5024\u306e\u7b26\u53f7\u3092\u53cd\u8ee2\u3055\u305b\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u6700\u5927\u5316\u554f\u984c\u306e\u6700\u9069\u5024\u306b\u623b\u3059<\/span>\r\n    <span class=\"n\">mean_MAPE_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">mean<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">stder_MAPE_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">stdev<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D06<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b9f\u9a13\u7d50\u679c\u3068\u3057\u3066\u3001MAPE \u306e\u554f\u984c\u30b5\u30a4\u30ba $N$ \u4f9d\u5b58\u6027\u3092\u793a\u3059\u30b0\u30e9\u30d5\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D06<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D06<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"o\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">xaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_major_locator<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">ticker<\/span><span class=\"o\">.<\/span><span class=\"n\">MaxNLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">integer<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>  <span class=\"c1\"># \u6a2a\u8ef8\u3092\u6574\u6570\u5024\u3067\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"MAPE\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$log_<\/span><span class=\"si\">{2}<\/span><span class=\"s2\">N$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$\\Delta=0.6$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h4><span class=\"ez-toc-section\" id=\"Delta10_%E3%81%AE%E5%A0%B4%E5%90%88\"><\/span>$\\Delta=1.0$ \u306e\u5834\u5408<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u554f\u984c\u30b5\u30a4\u30ba $ N=8,16,32,64 $ \u306e QKP \u3092\u30e9\u30f3\u30c0\u30e0\u306b 10 \u500b\u305a\u3064\u751f\u6210\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">Delta10<\/span> <span class=\"o\">=<\/span> <span class=\"mf\">1.0<\/span>\r\n\r\n<span class=\"n\">f_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">G_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">D_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">N<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">N_list<\/span><span class=\"p\">:<\/span>\r\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">):<\/span>\r\n        <span class=\"n\">f<\/span><span class=\"p\">,<\/span> <span class=\"n\">G<\/span><span class=\"p\">,<\/span> <span class=\"n\">D<\/span> <span class=\"o\">=<\/span> <span class=\"n\">make_QKP<\/span><span class=\"p\">(<\/span><span class=\"n\">N<\/span><span class=\"p\">,<\/span> <span class=\"n\">M<\/span><span class=\"p\">,<\/span> <span class=\"n\">Delta10<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">f_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">f<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">G_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">G<\/span><span class=\"p\">)<\/span>\r\n        <span class=\"n\">D_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">D<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"ADMM_%E3%82%A2%E3%83%AB%E3%82%B4%E3%83%AA%E3%82%BA%E3%83%A0%E3%81%AE%E5%AE%9F%E8%A1%8C-3\"><\/span>ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u751f\u6210\u3057\u305f\u305d\u308c\u305e\u308c\u306e QKP \u306b\u5bfe\u3057\u3066 ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_feas_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_ineq_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_feas<\/span><span class=\"p\">,<\/span> <span class=\"n\">E_ineq<\/span> <span class=\"o\">=<\/span> <span class=\"n\">qa_admm<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"n\">f_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">G_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">D_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">rho<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">M<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_nu<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">N_list<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span> <span class=\"o\">\/\/<\/span> <span class=\"n\">N_inst<\/span><span class=\"p\">],<\/span>\r\n        <span class=\"n\">t_max<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">t_conv<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">epsilon<\/span><span class=\"p\">,<\/span>\r\n        <span class=\"n\">gamma<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">x_feas_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_feas<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_ineq_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [17:31&lt;00:00, 26.29s\/it]\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"Gurobi_%E3%81%8B%E3%82%89%E5%8E%B3%E5%AF%86%E8%A7%A3%E3%82%92%E5%8F%96%E5%BE%97-3\"><\/span>Gurobi \u304b\u3089\u53b3\u5bc6\u89e3\u3092\u53d6\u5f97<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u7d9a\u3044\u3066\u305d\u308c\u305e\u308c\u306e QKP \u306b\u5bfe\u3057\u3066 Gurobi \u3092\u5b9f\u884c\u3057\u3001\u53b3\u5bc6\u89e3\u3092\u6c42\u3081\u3066\u3044\u304d\u307e\u3059\u3002\u3053\u306e\u51e6\u7406\u306b\u306f\u6570\u6642\u9593\u304b\u304b\u308a\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">x_opt_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n<span class=\"n\">E_opt_inst_D10<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">k<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">trange<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"n\">x_exact<\/span><span class=\"p\">,<\/span> <span class=\"n\">val_opt<\/span> <span class=\"o\">=<\/span> <span class=\"n\">grb_exact_qkp<\/span><span class=\"p\">(<\/span><span class=\"n\">f_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">],<\/span> <span class=\"n\">G_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">],<\/span> <span class=\"n\">D_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">k<\/span><span class=\"p\">][<\/span><span class=\"mi\">0<\/span><span class=\"p\">])<\/span>\r\n    <span class=\"n\">x_opt_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">x_exact<\/span><span class=\"p\">)<\/span>\r\n    <span class=\"n\">E_opt_inst_D10<\/span><span class=\"o\">.<\/span><span class=\"n\">append<\/span><span class=\"p\">(<\/span><span class=\"n\">val_opt<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_subarea output_stream output_stderr output_text\">\n<pre>100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588| 40\/40 [6:32:52&lt;00:00, 589.31s\/it]   \r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h5><span class=\"ez-toc-section\" id=\"%E7%B5%90%E6%9E%9C%E3%81%AE%E6%AF%94%E8%BC%83-3\"><\/span>\u7d50\u679c\u306e\u6bd4\u8f03<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5f0f (9) \u306b\u57fa\u3065\u304d\u3001\u554f\u984c\u30b5\u30a4\u30ba\u3054\u3068\u306bMAPE \u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5e73\u5747\u304a\u3088\u3073\u6a19\u6e96\u504f\u5dee\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">mean_MAPE_D10<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">stder_MAPE_D10<\/span> <span class=\"o\">=<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">zeros<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">)<\/span>\r\n\r\n<span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">len_N_list<\/span><span class=\"p\">):<\/span>\r\n    <span class=\"c1\"># \u6700\u9069\u5024\u306e\u7b26\u53f7\u3092\u53cd\u8ee2\u3055\u305b\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u6700\u5927\u5316\u554f\u984c\u306e\u6700\u9069\u5024\u306b\u623b\u3059<\/span>\r\n    <span class=\"n\">mean_MAPE_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">mean<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span>\r\n    <span class=\"n\">stder_MAPE_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">]<\/span> <span class=\"o\">=<\/span> <span class=\"n\">stdev<\/span><span class=\"p\">(<\/span>\r\n        <span class=\"p\">[<\/span>\r\n            <span class=\"nb\">abs<\/span><span class=\"p\">(<\/span><span class=\"n\">E_ineq_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"o\">-<\/span> <span class=\"n\">E_opt_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">])<\/span>\r\n            <span class=\"o\">\/<\/span> <span class=\"o\">-<\/span><span class=\"n\">E_opt_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">]<\/span>\r\n            <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nb\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n            <span class=\"k\">if<\/span> <span class=\"n\">E_ineq_inst_D10<\/span><span class=\"p\">[<\/span><span class=\"n\">N_inst<\/span> <span class=\"o\">*<\/span> <span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"n\">j<\/span><span class=\"p\">][<\/span><span class=\"o\">-<\/span><span class=\"mi\">1<\/span><span class=\"p\">]<\/span> <span class=\"ow\">is<\/span> <span class=\"ow\">not<\/span> <span class=\"kc\">None<\/span>\r\n        <span class=\"p\">]<\/span>\r\n    <span class=\"p\">)<\/span> <span class=\"o\">\/<\/span> <span class=\"n\">np<\/span><span class=\"o\">.<\/span><span class=\"n\">sqrt<\/span><span class=\"p\">(<\/span><span class=\"n\">N_inst<\/span><span class=\"p\">)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5b9f\u9a13\u7d50\u679c\u3068\u3057\u3066\u3001MAPE \u306e\u554f\u984c\u30b5\u30a4\u30ba $N$ \u4f9d\u5b58\u6027\u3092\u793a\u3059\u30b0\u30e9\u30d5\u3092\u8868\u793a\u3057\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"o\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">xaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_major_locator<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">ticker<\/span><span class=\"o\">.<\/span><span class=\"n\">MaxNLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">integer<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>  <span class=\"c1\"># \u6a2a\u8ef8\u3092\u6574\u6570\u5024\u3067\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"MAPE\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$log_<\/span><span class=\"si\">{2}<\/span><span class=\"s2\">N$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">title<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$\\Delta=1.0$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">show<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3><span class=\"ez-toc-section\" id=\"%E5%AE%9F%E9%A8%93%E7%B5%90%E6%9E%9C%E3%81%AE%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u5b9f\u9a13\u7d50\u679c\u306e\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\Delta = 0.2, 0.6, 1.0$ \u306e\u5834\u5408\u305d\u308c\u305e\u308c\u306b\u3064\u3044\u3066\u3001MAPE \u306e\u554f\u984c\u30b5\u30a4\u30ba\u4f9d\u5b58\u6027\u3092\u6c42\u3081\u3066\u304d\u307e\u3057\u305f\u3002\u6700\u5f8c\u306b\u3001\u5404 $\\Delta$ \u306b\u304a\u3051\u308b\u7d50\u679c\u3092\u540c\u3058\u30b0\u30e9\u30d5\u306b\u30d7\u30ed\u30c3\u30c8\u3057\u3066\u6bd4\u8f03\u3057\u3066\u307f\u307e\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing code_cell rendered\">\n<div class=\"input\">\n<div class=\"inner_cell\">\n<div class=\"input_area\">\n<div class=\"highlight hl-ipython3\">\n<pre><span><\/span><span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D02<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D02<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"solid\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"o\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"$\\Delta=0.2$\"<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D06<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D06<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"dashed\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"x\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"$\\Delta=0.6$\"<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">errorbar<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">log2N_list<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">mean_MAPE_D10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">yerr<\/span><span class=\"o\">=<\/span><span class=\"n\">stder_MAPE_D10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">linestyle<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"dotted\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">marker<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"v\"<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capthick<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">capsize<\/span><span class=\"o\">=<\/span><span class=\"mi\">10<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">lw<\/span><span class=\"o\">=<\/span><span class=\"mi\">1<\/span><span class=\"p\">,<\/span>\r\n    <span class=\"n\">label<\/span><span class=\"o\">=<\/span><span class=\"s2\">\"$\\Delta=1.0$\"<\/span><span class=\"p\">,<\/span>\r\n<span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">gca<\/span><span class=\"p\">()<\/span><span class=\"o\">.<\/span><span class=\"n\">xaxis<\/span><span class=\"o\">.<\/span><span class=\"n\">set_major_locator<\/span><span class=\"p\">(<\/span>\r\n    <span class=\"n\">ticker<\/span><span class=\"o\">.<\/span><span class=\"n\">MaxNLocator<\/span><span class=\"p\">(<\/span><span class=\"n\">integer<\/span><span class=\"o\">=<\/span><span class=\"kc\">True<\/span><span class=\"p\">)<\/span>\r\n<span class=\"p\">)<\/span>  <span class=\"c1\"># \u6a2a\u8ef8\u3092\u6574\u6570\u5024\u3067\u8868\u793a<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">xlabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"$log_<\/span><span class=\"si\">{2}<\/span><span class=\"s2\">N$\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">ylabel<\/span><span class=\"p\">(<\/span><span class=\"s2\">\"MAPE\"<\/span><span class=\"p\">)<\/span>\r\n<span class=\"n\">plt<\/span><span class=\"o\">.<\/span><span class=\"n\">legend<\/span><span class=\"p\">()<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"output_wrapper\">\n<div class=\"output\">\n<div class=\"output_area\">\n<div class=\"prompt output_prompt\">Out[\u00a0]:<\/div>\n<div class=\"output_text output_subarea output_execute_result\">\n<pre>&lt;matplotlib.legend.Legend at 0x7f7c9bf53c70&gt;<\/pre>\n<\/div>\n<\/div>\n<div class=\"output_area\">\n<div class=\"prompt\"><\/div>\n<div class=\"output_png output_subarea\"><img decoding=\"async\" alt=\"No description has been provided for this image\" 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UUi2VUl5KqSCl1EygIbDOhfGWKCwwDMBppQi4dI3rgICAwkf79u0L36+s9957j4CAAAYPHozFYim8xtGjRwv3mTRpEjfddFPh6+nTp3PrrbfSrVs3wsPDsVgsVyzBCCEqLyMvg40nNtKqTisW3OC40re9XDktx2ygDvAr4AdsAO4DUErdCyzSWgfZ9u0ELAXqA5lAHDBIa33chfG6zerVq51+jbFjx15WbVXcwoULL3ltMpmYN28e8+bNc2JkQoiizuecJzY5lr5N+xZ2nHEll11Ra20Bptoexd9bDiwv8voV4BVXxVagPPXkBYPqrkTqyYUQFXUo9RBrDq1hStcpTOk6xW1xyAR\/Rdg7wZ8QQjhTviWfxrUa07NJT3eHInM3CSGEJ4k\/Hc\/Un6YS6BNIj8Y93B2OlCSEEMIT5FnyOJZ+jE5hnXih9wvuDqdQjSpJWK1Wd4dQo8jvWwj77UvZxwd\/fIBSihC\/4kPK3KfGlCRq1apFYmIiDRs2xMfHB6WUu0OqtrTW5Ofnk5ycTK1atdwdjhAeLSEtgV1ndjGs5TCnThhaUTUmSTRt2pSzZ89y9OhRzGazu8Op9ry9vQkJCaF+feeNJxGiqtNa42vyvWzyUE9SY5KEl5cXDRo0oEGDBu4ORQgh2HZyG98e\/Za\/9\/g7TYKauDucUtWYJCGEEJ7Aqq2k5aYR3SCaJrU8NzkU8NwyjhBCVEM\/Hv+R13a+hp\/Jj4jgCHeHUyYpSQghhAskZyaTmJFI\/4j+9Gvaz93h2E1KEkII4QKJGYnsS9mHUsotczBVVNWJVAghqqBtJ7dx4PwBRl8zmi4Nu7g7nHKTJCGEEE6gtcZsNRMVHEUtn6o7XkiShBBCOMGXh79k\/7n9TO02lYa1Glb8RD\/Mgp9ml7nbHoCZdozUvm469J9h9+UlSQghhAOl56WTnpvOkKghDIgcUPkT9p9h1029w7IO7Bmzp\/LXK0YaroUQwoE2ntjIuoR1+Jh8qnQ1UwEpSQghhAPsPL2TC3kXuLnFze4OxaGkJCGEEA5gUiZMyuTuMBxOShJCCFEJn\/35Gel56YxpN8bdoTiFJAkhhKiAHHMOFm2hX9N+aLS7w3Eal1U3KaVMSqm5SqkzSqkLSqlPlVJlziOtlHpIKaWVUs+6Ik4hhLDHR398xMr9K6kXUI\/6AdV3SnxXliSmA8OA7kAK8DbwHnBTaQcopZoBT2LrAiyEEO725\/k\/8VJejL5mtEevA+EorvwXTgDmaK0Pa63TgKeBIUqpqCscswT4O3DOBfEJIUSZDpw\/wJG0I5i8TB6xwuXnOxPpPft7Lvw+i96zv+fznYkOPb9LShJKqRAgEthRsE1rfUgplQ50BBJKOGYikKW1\/lgp9VAZ55+AkYSIjIx0YORCCGFYfXA1gT6BHtXF9fOdicxYtYfsfAugSEzNZsYqo+JleOdwh1zDVSWJYNtzWrHtqUXeK6SUigSeBa6YHAporRdrrWO01jFhYWGViVMIIS5htpqxWC20rduWtnXbujucS8xdt9+WIC7Kzrcwd91+h13DVW0SF2zPxScWCQXSS9j\/LeAlrbVjy01CCFFOC3ctpEFgA0a1GeXuUC6TlJpdru0V4ZIkobVOVUodA7oA8QBKqRYYpYjdJRwyCOiqlPqX7XUI0E0pNVhr3dcFIQsharikjCQCvQMZ224sft5+7g7nEll5Zj6NS8TkpTBbL+9+2yQ0wGHXcmXD9WJgmlKquVIqGJgDrNNaJ5SwbwTQCYi2PWKB\/wEjXRKpEKLG++LQF2w7tY0g3yB8vHzcHQ4Ayek5vPzNH\/SZ8wMbD5xh0nUtCPC59DYe4GPiqcFtHHZNV3aBnQ3UAX4F\/IANwH0ASql7gUVa6yAArfWJogcqpXKBdK11sgvjFULUQBuObqBpUFMmdpro7lAK7U1MY8mmI3z\/x2mGRzdh1UO9iKpvTB7YskFt5q7bT2JqFuGhgTw1uI3DGq3BhUlCa20Bptoexd9bDiy\/wrHXOy8yIYS4yFt5e0TXVqtV8\/0fp3lr02GOpmQxplcUM29tR0jgpaWa4Z3DGd45nA7LOrDZCVOFy7QcQggBvBb3Gu3qt2Ng5EC3xpGVZ+bTHSd4e3MCtf29eaBPc4Z2aIyPyT0D98pMEkqp2lrrC1d4v53W+jfHhiWEEK6RlptGoE8gI1qNoJ5\/PbfFcSoth2VbE\/ho+zGubV6Xl0d2JKZZHbeXauwpSSRSZCyDUipeax1d5P2tlDDWQQghqoJX416lT3gfx6wiVwF7E9N4a+Nhfth\/hhGdw\/n8b71pVs9zFiuyJ0kUT2PNynhfiEoZuWYk+89fHAzUYVkHANrUacMnf\/nEXWGJaubXU7\/SPKQ5M7rPcHnvJYtV893vySzZdITj54z2hueHtSckwDN6URVlT5Io3gm3rNdCVEqnBp04nHaYfGt+4TYfLx+iG0S7LyhR7ew9uxdfk69LZ3DNyjPzyY4TvL3pCCEBPjzQtwU3tW\/ktvYGe0jDtfA4kzpOYvXB1Zds81JeTOo0yU0Riepk0a5F9GrSi3Htx7nsmifTslm25Sgf\/3qM7s3rMe+OTnS1s71hfvx8FuxaYNd1CkrdV\/JQp4eYHD3ZrvOBfUnCRyl1NxerlYq\/lkQjHCosMIxhLYex6sAqzNqMj5cPfcP7EuJXfFYXIeyXb8nHx+RD14Zdiagd4ZJr7j6RypJNR\/hx\/xlu6xLO6r\/1IbJeYLnOMTl6sn039ZkhMLP49HiVZ88NPhn4d5HXZ4u9lgFuwuHGtx\/P6oOrMVvMeCkv0vPSycrPIjM\/E4u2uOyPXFQff9\/0d25vfTvdG3d36nUsVs23tvaGxPPZjOnVjBc8tL3BHmUmCa11lAviEKLQ8QvHeXbTswy7ahgrDqxgeMvhPNvDWJhw28ltnM0+yz1X38PWpK3ENIrxmCkThGc6lHqIyNqRPNP9GaeWRjNzzayMPc7SLQmEBvryYJ\/m3NS+Ed4e3N5gD7uqipRSLYEOQLzW+ohzQxI1WWZ+JhG1I5h33TwAVhxYcUlbxI1RNwKQZ8lj5YGVxDSM4c\/zf+Jr8qVZcPGOd0LAe\/ve47ZWt9ExrKNTzp+Ums2yrQms+PU4PVrU47+jOtEl0v3jGxzFnsF0twEfAyYgTyl1m9b6K6dHJmqcjLwMRn89mg9v\/pCwwIvrgpTU+8TX5Mt\/r\/8vAPvP78fby5vI2pGsP7qeGyJvwORlclncwjOt2L+C65pex8xeM51y\/t0nUnlr4xF+OnCG27s0Zc3DfYioW772hqrAnpLEs8AzwHzgYdvPkiSEQyVlJNEkqAkf3PwB\/t7+5Tr2lha3AJCel87WpK3c2OxG4k\/HE+oXSlRIlBOiFVWBj5cP2sE99C1WzYZ9ySzZdJik1BzG9Y7ipRHtCfavvlWe9lSWNQf+o7XOBP4LtHRuSKKmsVgtTPt5GsmZyQR4V3we\/GDfYGb2molSioT0BJKzksm35PPZn5+htQznqSmmb5zOH+f+YESrETSq1cgh58zINbN08xH6z\/uRhT8dYkyvKH566noe7NuiWicIsK8kYdJaWwG01vlKKV8nxyRqkH0p+2gV2oplNy3DSzmugW94y+EAnM0+y4mMEyil+PnEzzQLbiZtF9VUSnYKdf3rMqHDBId9xkmp2SzbksCK2OP0vKoer9wZTddmdRxy7qrCniThq5R6pshr\/2Kv0Vr\/GyEqYMX+Fdzd9m7a1HXcIilF1Q+ozyOdHwGMhNEgsAHpeel8c+Qbj1yOUlTcjI0zeDLmSYf8X4o\/boxv2Phn9W5vsIc9SeIXjOVEC2wr9lpz6bgJIcoUlxxHeFC40xoVS3Jbq9sAOJV5qnDKjy8OfUF0WDQRwTLuAso3utce5R3dWxE\/Hf+J7o27878b\/lep7tBGe8Mp3tp4hJNpRnvDv0e0p3Y1r04qiz3jJK53QRyihvn93O9oNA1rNXT5tRvVasS9V98LQK4lF5OXiaSMJDYlbqrxpYvcMzdw4XfHVcflNmnlsHOVRGtNbHIsLUJbVHiAZUaumRW\/HmfpliOEBfnxYN8W3HhNwyo\/vsFRKjylhjI6AQ8FJmqt\/+K4kER1FnsqFqu2Ft6k3W1ka2PZ9BMXThDoY1QnLP99Of0j+tMkqIk7Q3OLKYNaM2VQ6zL367CsA3ucsAqavbTWzNo+i3HtxvFkzJMVOkdiajbvbD7Cyh0n6N2yPq\/e1ZkukVWsvWHT\/0F4F2je7+K2Iz9DYhz0edwhlyh3klBKNQEeBB4AGgMrHBKJqBE0Gou2uDuMyzSt3ZSmtZsC4G\/yp5ZPLfaf28\/us7u5o\/Udbo5OFFUwB1Pf8L7U8S\/\/TX3nsfMs2XSETQfPMrJLU76oyu0N4V1g5Vi44x3j9ZGfL33tAPaOuFbATcAEjNLDGaAO0FVr7b6vE6LK2HVmF3vO7OG+a+5zdyhlur317YCxYlmjQKML5Wtxr3HP1fe4dFppcTmtNePWjWNW31n0bdrX7uMsVs36307x1qYjJKfnMK53c2bd1qHqtzc072ckhJVjjdcFCaJoyaKSyqx0U0o9CxwBPrdtuh1j4aE0yjG5n1LKpJSaq5Q6o5S6oJT6VClV4l+cUqqvUipOKXVOKZVm+\/k2e68lPE+jwEa0rlN2NYYniQyOpG\/TvmitiQyOJMQ3hG0nt\/HZn5+5O7Qaaf85YyGqNwa8YXf7w4WcfJZsOsJ1c3\/grU1HeLBPc36cej0P9Gle9RNEgYbtIbyr8XPMAw5NEGDfYLoXgFrAcK31cK31F1prcwWuNR0YBnQHmtq2vVfKvvuBEUA9IBR4HHhfKXV1Ba4r3Ojg+YP8c8s\/aVirIdc2vtbd4VSIUorhLYfjY\/KhUa1GNA9pjtaamVtmkpbr+KmZxeWs2srrO1\/nVOYpQv1Dy9z\/xPksXvpyH31f\/oGdx87z+t2d+fShXtzUoXH1aZDWGnZ9BK91MaqZAGKXXPzZQez5bd0P7AO+UErFK6UeUUrVpfwr0k0A5mitD2ut04CngSFKqajiO2qtT2utj2pjmKwCrLZYZbR3FaK1pllws2pVp98suBnRDaKxaiu9w3sT7BvMNwnf8MWhL9wdWrVk1VaW7l1KjjmHNwa+QeOgxlfcP+7Yef72QRy3vL4JLy\/F2kf78sY9Xehc1Rqk7bH3U\/hxDmCFe1ca2wqqnhyYKMpMElrr97XW1wHtgR+BfwKJQH0gxp6LKKVCgEhgR5HzHgLSgVKnZlRKpQK5wEaM8RnrS9lvglIqVikVe+bMGXtCEk52Nvss9399P0op2tdv7+5wHM7kZWJQs0EopWhXtx1t67Yl35LPlB+mkGvJdXd41YZC4ePlc8XODmaLlbW7T3Lb\/M089tFOukbWYdO0ATwz9GrCQys+zYtHys+G7\/8FB9bBNcOhy2i48\/2LVUwFbRSJcQ67pN29m7TWvwOPK6WmAaOAicCXSqkdWutuZRwebHsuXjZPLfJeSdcMVUr5YTSatwFKrObSWi8GFgPExMTIJD1ulmvJpX5AfWb1nYW3V\/VfuLBgIJ7ZaubOtnfiZ\/Ljg98\/oG5AXYZEDXFzdFWT2Wpm8reT+Xfff5fa2eFCTj4f\/3qcpZsTaBziz4R+LRh0TSNMXtVjiu7LHPwO1j4JjTpAzDgweUPfJy7fr3k\/1zZcF6e1ztVav6e17gO0AzbZcdgF23PxFT9CMUoTZV3vc+A6jK63woPlWfK468u7SM9LL+xSWlN4e3nTo3EPAPo17UfH+h1Jz0tn0reTsBrTnwk7nMs5h7eXN1O7TaWef73L3j9+LosXbe0Nu06k8b97u\/DJQ70Y0r5x9UwQVqvxiH0bbpoDd74Hwa4bw2PPehKH7TjPlCu9qbVOVUodA7oA8bbztsAoRey24\/xgxOrc4ZuiUs5mn6V+QH3eveldavvWdnc4blWQIM1WM49EP4KX8uK1uNfoGNaR6yOud29wHizfms+E9RN488Y3L+sNt+PoeZZsOszWQymMiolg7aN9q191UlFWC8S+TfJPS+iZ8nes3APxZmBtKQd8ANNLe++ixwa2smvAZAF76gKiMBqulwKn7D7z5RYD05RSPwApwBxgndY6ofiOSqnbgQPA77YYRwMDgLmVuL5wIq01U3+aysyeM2UNhyK8vbxpV78dAKPajMLX5EtSRhIvbH2BhYMWujk6z6G15ttj3zIwciAf3vJh4RxMZouVdb8l89amw6Rk5PHX3lG8PLITQX7VvBozeR+seRhMvjQcs5TDDezo2DkzBGY6vredPb\/pHsB44O8YDddvAt\/o8k\/QPxtjAN6vgB+wAbgPQCl1L7BIax1k27exbf\/GQB5Gl9i7tdYbynlN4QJH0o4QHhTOWze+VSPaICqqYG0Di9XC09c+DcA\/t\/yToc2Hcm0jo3twdVnysrzMVjNbk7bSvXF3gn2DSc\/JN+ZT2pxAeGgAE\/tdxaBrGlbP6qSici+A8gJzDnQdB9H3gpd7u+wqe+\/1Sqkg4G6MrqwNgLeA12zdWT1GTEyMjo2NdXcYNcpLv7zEkKghxDSyq7Ob4YdZ8NNsxwVx3XToP8Nx53ORs9lnCfQOJCE9gQXxC3h94OtorT0+WThq7qZcSy7\/3vZvnu72NLV8anH8XBZLNyfwadwJrmsdxgN9mtMpIrTyAXs6reH3L+Cb6XDji9D+9vKfo5IlCVsnpMv+iO1OEkVOZAL+gbGs6Y1a6+8rHJUTSJJwnQPnD1Dbp3aZfdcrw90TybmK1prkrGQa1WrEw989zMSOE2lXvx0K5ZEJwxGfS741Hx8vH74\/+j21dUfe3nSUXw6nMKpbBGN6RtGkOrc3FGW1wMf3QcohuOUViOpdsfM4KUnYXTdgG\/T2IDAWOGr7eXOFIxJV3s7knYQFhjk1SdQUSqnC6qiXer9ELd9a\/HLyFz7\/83Nevu5lzFZztarKyzZnc+\/ae7knYi7vb\/XjfNYe\/tq7OfPu6ESt6t7eUMCcB8e2QovroNuDENUXvD1v4U97ejeNxGiT6AwsBwZrrX9zdmDCc\/15\/k9SclK4s+2d7g6lWiqYdqJn455cU\/caAMZ8PYYX+7xIRO0ITMrk0KVeXS325G\/E\/enPyT\/GseLUaR66\/ipuuLoGtDcUdXQLfPkE1IkykkPLge6OqFT2pOwVGL2bFgI5wDCl1LCiO8jypTXLhbwLpOakujuMak8pVZgwFg1aRC2fWqw7uo5fkn5hZq+ZZJuzCfCuOlUyx1KyeHPz73ye9C+uD3maxff2o0PT4kOnaoA9n8D6f8CQWXDNMPDA6sSi7EkSP2PM01TavLyyfGkNcTjtMJsTNzP6mtHuDqXGCfI1Ov4NiRpCv\/B+aK2568u7eOvGtwjyDcLHy8cjq6O01uw4ep5FP\/\/B9nNruLP1aNbfvZzGIVUnuTmE1hD\/gTFauvVgaHUj+Jc62YRHkeVLhd2CfYNpUqvmrdbmaQpW0Ftx6wr8TH6s+nMVh1MPM7XbVNJy0wjxc\/+383yLla\/3nmLJxsOkZeczpncE3Wq1Zlz71viYqskU3fY6sx++nAJ5mTDsf+BXtQaaet5XD+FxkjKSWLR7ETN7zmRgM8+tO61p\/Ex+ANzW6jbyrfnkW\/O5Z+09fHzLx1i0hUDvQJffkNOy8\/lo+zGWbUkgom4gf+3XiDUnZ3Fv9wX4mv7q0lg8gtUCnzwAXe6Hbg+Al8ndEZWbJAlxRVprwgLDGNp8qEd2xRSGghHKa4avweRl4r1975FjzmF8x\/EkZybTsFZDh1zn852JzF23nwups+g9+3ueGtyG4Z3DOZqSydLNCXy2M5EBbRuw+P4YmtSzUNe\/LldHTMPX5Hm9dpzqzw0Qvxxufxsm\/lQlk0OBqttFQjjdhbwLjFs3DovVQvfG3d0djrCDyXYzGn3NaB7o8ACZ+ZlM+nYS+ZZ8zmSdqdQ05p\/vTGTGqj0kpmYDisTUbJ7+dDe3vr6REfO3EOBrYt3j\/XjlzmjC61mZsH4C+db8KrciYaWkn4QVY+Crp6DzfcZo6SqcIEBKEqIU+dZ8avvW5h89\/oG\/t7+7wxEV4KW8qOVTi1V\/WYVSis8Pfk6ofygjW40kIT2B5iHNy3W+uev2k51\/6boOeWYrx85ls3XGAAJ9vcm35vP9se8ZEDngkjmYqj2r7feSFAf1W8GIheBTPRrnpSQhLmOxWrjvq\/s4k3WGq0Kvcnc4opIKqgnHdxzPyFYjSclJ4fmtz6O15nj6cbLys+w6T1Jqdonb07PzCfQ1vm9m5mWyOXEzZqu55iSIxDh4cwD8vgba3gwDnq02CQIkSYhi0vPSMXmZWHDDAsICw9wdjnAwpRT1A+rzzpB3UErx2cHP2HpyK2armX0p+0o9TmtNSEDJN\/0moQGczT7Li1tfNEqfPf\/hkd1xHc6Sb1QrfXAndJ9krBRXDUmSEJd4+uen+S3lN+r613V3KMIFHu3yKAMjB5KUkcTSvUsB2H9uPxl5GYX7pGbl8dD7cQT6mvDzvvSWEeBj4okbryLUL5Q+4X0K20SqNa3h3BHw8oZ6reBv2yD6bo8fFFdRNSDdC3ucyjxFHf86vNb\/tZrXE0UQGRzJ3OuM5Vq+PPwlAyMH0qpOK1b\/toP\/fWNmcLtGnAmZxYXz+yn+v2P2Pn9GdN5G\/8j+rg\/c1c4dNkoPuRfgr+ug+wR3R+R0UpIQACz7bRlbErdIghA8GfMk7et1ZNaGzby86WNeGt6em6\/Npl29ay5rZ\/Dx8mFI1JAqPZeU3fathjcHGnMtjV1bbUsOxUlJooZLykhCo3m629MyDkIAcOJ8Fo9\/FE+Abwjr7\/8PDYL9mbN9KSNajWDt4UuXx\/RSXjzW9TE3ReoiRzZCvasgPAYm\/Ah1mrk7IpeqAelfXMm2k9v4JekXSRACgLW7TzLsjc3c2K4hy8ZdS4Ngo\/vztGun0blBZ\/o17VdYavDx8mF4y+HUD6jvzpCdJ\/MsfPYQfDYR0k5ASHiNSxAgJYka61TmKRLSExjRaoRbrj8\/fj4Ldi2wa98OyzqUuc9DnR5icvTkyoZVY2XlmXl+zT62HUlh6bhudGwaWuJ+z3R\/ho2JG8m15OKlvJjUaZJrA3UVcx68NRDa3mI0TFex+ZYcSZJEDXU66zRH0o7Qo3EPt1x\/cvRk+27qTlrcXVz0W1Iaj3y4k+iIUL58tC9BV1j0JywwjGEth7Fi\/4rqWYpI3mcsI3r9NKNqKaCOuyNyO6luqmGSM5NZ\/vtyOoZ15O62d7s7HOFGWmuWbDrC\/Uu289jAVvx3VPQVE0SBSR2N0kO1KkXkZcKG52DZLVCrntHNVRIE4MKShG1t7NkYy5\/6A+uBiVrrsyXsOxSYCnQETMBe4Bmt9UZXxVtdeXt5V6mFaoRznM3I5amVuziXlc9nk3sTWS\/Q7mMLBllWq1LEro8gPQke2gq1HTMZYnXhypLEdGAY0B1oatv2Xin71gFeB1oCYcAHwNdKqQhnB1ldnc85z4tbXyTEL4TbWt3m7nCEG2388ww3v7aRqxsH88mknuVKENVKWiJ8fB8c\/BZi\/gq3vyUJogSubJOYALygtT4MoJR6GjiolIrSWicU3VFrvbzYsQuUUi8AMcBxVwRb3dT2rU3v8N41Y7oEUaI8s5X\/rN\/P6vgkXhkVTa+W1agkUB4WM2xfDD\/PhWsnQLM+NWbMQ0W4pCShlAoBIoEdBdu01oeAdIwqpbKO7wjUw6h2Kun9CUqpWKVU7JkzZxwTdDWRa8ll0reTyDJnMSBygLvDEW6ScDaTkQu3cOhMBl891rfmJoi8TOP53CF4YD30nwE+MsvxlbiquqlgMdfi3VRSi7xXIqVUA+AT4GWt9Z8l7aO1Xqy1jtFax4SFyaR0Bazaip\/Jj0c6P0Kwb9VYT1c43qq4E9y2YAu3d2nKm\/fHULdWDRxVn50KXz4B7w4z1ne4+T\/GlN6iTK6qe7hgey6++G4oRmmiREqpJsAGjEbuGRW++g+z4KfZFT78MtdNN76BeDCtNePXj+e5ns\/Rrl47d4cj3OBCTj7\/+Hwve5PSWf5gd65ubMcXBTv\/VvaA0T25LJ7wt3LwW\/j8b9B2KNy7UqqWyktr7ZIHcBT4a5HXLQANRJWyfxRwCJhXnut07dpVV9g\/gyt+rAfJzMvUVqtVn8w46e5QKmbjK1of\/sn4ueAzOfyTsV3YJe7oOd13zvd6xqrdOivX7PDzt3+nvcPP6XBnD2qdc0HrpF1aH9vu7micr5L3LyBWl3BPdWXvpsXANKVUc6VUMDAHWKeLNVoDKKXaApuAD7XWU10YY7Xwzy3\/ZNupbTSq1cjdoVRMeBdYORaO\/Gy8PvKz8Tq8izujqhKsVs38Hw8y\/t1Ynhnaln+P6ECAbw2Yvrsocy78OAfeugFOxkPjjhDRzd1RVVmu7OoyG6Nr66+AH0Y10n0ASql7gUVa6yDbvtOAcOBxpdTjRc4xUV\/e80nYpOak4u\/tz\/O9nq\/aYyGa9zO6I358n\/F65Vi44x1juyhVcnoOUz6Ox2zRrHm4D01Cq\/D\/gYrKz4FF\/Yz2hok\/Q2g16DVfnupyJ1QBKqOUUX3ExMTo2NjYih1cxaeAeGPnG4QHhbttPqZKyT4POWlQJwo+eQAOfAPe\/pB1Fvo9DZmnIfUYRPaCZj2NZy+ZMKDAt\/uSmb5qD6N7NOPhAS0xeTm33r3Dsg7sGbPHqdcol4wzcOQn6DDSmFqj4TXujqjKUUrt0FrHFN8uneargdScVDLyM5gcPRlFFWiU09pY+lEpWPskHN9mzLLZfSIMfA56Pwbtb4c1Dxv7xy6BW18z9j+6BTb+B+7rDb99Bkk7jYQR2b1GTqOQk29h9td\/sGFfMgvv60JMVA1bUdBqhbhl8P1L0OV+I0lIgnAoSRLVwC+nfuHEhRM82OFBd4dSuqxzEL8cjv0Cx7dDr0eg96NGO0PXsdCoA5hsC9rkpBoJ4o53YNmtxnNBldPgf108Z71WcGY\/\/DIfPn3AmK3TnGtLHD2NqZ2rsT+TL\/DIhzu5KiyIrx7tS0hgyWtQV2u\/\/A\/2rYH7V0Oj9u6OplqSJFGFpeWmsf\/cfoZEDXF3KJfKSTO+8RckhOueNpLA+QRjsfghsyDEVlfcdezlxyfGXdoG0byf8Tox7tJ2iUbtL94YLPnGmsNJcUYJ4+unwbcWjFwKDdtD6lGo37padH\/UWvPh9uPMW7+faUPaMComomatB5KbYdTRdxgF3cZDj79J1aMTSZKowpIyktiRvINrG1\/rviC0hpSDtoSwDW54HpL3wLZFENnDSBAR1xo37Jv\/Y985+zx++bbm\/a7ccF1QCgnvCnctN+I6+yfUbmQkiOUjjdG2kT2hx0MQ1QesFmNgVRWSmpXH9E\/3cOxcFism9qRlg6CyD6pO\/lgLX0+DZr2hdmMZLe0CkiSqoPS8dL4+\/DWj2ozi6npXu\/bi+TlGdU7yXrh2PGz6L8S+Y7QJRHQ3brotrjce7qQUhLU2fvYPhsf3GBO6HdsKfsFGwvjP1dAkGpr1gtaDoUlnt4Zclu1HzjHl43gGt2vEq3dH4+ddtRJcpWgN+dmwbSEMny893VxIkkQVZLFayDZnu+ZiGach7bjxDX3d3yH2baPaJrKHMVFar8eg75OuiaWyQsKNhs0Cj++CY9uMxHFyl5EkPnnAKH006wURPYy1BdzMbLHy+vcH+WD7MV6+vSP92zZw2rVe2XCAV78rcfabYmYTNX1tmXs9NrAVUwa1rnhAlnz4ZQEkbDRGS4\/5ouLnEhUiXWCL8vAusFn5WbwR\/waPdXkMP5Of4y9gtUJuOgSEGglh\/1eQlQJtb4Xh\/zN6IAXUMaqOXMXVn0nCZlt7ylbwCTCqruI\/AGUyut6GRrouFuDE+Swe\/ygefx8T\/x3VqXDNaXdzSRfYEztgzSMQ1MCoqqx3lXOvV8NJF9hqwM\/kx9V1r8bXy4ETtFnyYfOrRnvC8e3Q\/ja45RW4qj9E3wthbS82CoY0vfK5qoOo3sajKGWCP76E9X+HoIYwaROc+cOoAin6+3GwtbtP8tzqvUzo14LxfVvg5eSxDx4j+7xRJZh1Fvo+YXSHrkkN8x5GkkQVYLFamLZxGtOvnc6tV91a8RPlZcKf640qluPboN0IoyuqORc6j4a\/vHFx0ZWWNzgm+Oqg053GQ2vISDZuWMe2wubXjBtaZA+4bbHRu8rLB7wrl8Sz8sy88MU+fjmcwttju9EpItQx\/w5PpzXsXgEb\/gEj3zbaiYTbSZLwcFprTF4m7m57N3X9yzFQymqB0\/sudkO9drxRVbLrI6OBefC\/jDp4pWDA3533D6hOlDLaK8BYySzmr3DhlPH79QuGXR\/C2qnG77VZT4h5AIIbl+sS+5LSeeTDODpFhPLlo33tWnO6WsjNgI\/uNpLuXR9C067ujkjY1JD\/gVXXkz89yfgO4+nasIw\/mtwMSIw1Sgk9Jhl16xv+YTS+Nu9rTHcR1ADu+dglcdcYtRvBNX8xfo6+B9reDMd\/hWNbQFuNBPLVU0ZDeGQPiOoLgZcne601Szcn8MYPB3nulmsY3rl6DwQslJ8Dp\/ZA0xhjlbjWN4FJbkueRD4ND5VnycPHy4cpXacQHlTCDSP1uPHH1XaoMSbh2+eNAWuR3cGcB21uMt4TruUfAq1uMB4AterDkNlG9dTO943qqBbXGX39I3tCs56k+DThqU\/3kJKZx2eTe9Gsngs7BrjToe+NaVkiexqztF5diapU4TSSJDzUnO1z6NGkB4OaDTK6ml44YVQXbfwP\/LrEaEeI7AGtBkGnu4yRy95O6PEkKsfbz6h6atbz4rbcC9C4Exz8ltz1z\/N5bl\/aXvsUTzTahXd+MFivqXKD\/Mpt63zYtgCGzpO2Bw8nScLDZOVngdXK410fp9b2t+HH1yBxp1FCuO9TaHWjMbVF3RYXe3yY7JgeWHgOv9rkdXmA\/6T0YbU5kVfuvJqerRrD2gWwca4xNiVmHAx6Hs4dhtpNqsfIYqsFdrxjlHI7jjK+2PgGujsqUQZJEp7AaoE9n8DxX1hxciPUbsTYu740qip6PgxNu12sx27Uwb2xikpLOJvJox\/tpEFtP756vN\/FNadvfdV4zjhjjE8B+O4FOLDeWDin5UDo95QxnqWqzVV0chd8OQVMvsZo\/OAm7o5I2EmShKtZ8o0\/mOPbjJ5HrQZB59FkH\/6Bc\/WiGN1pwcVE0Ple98YqHG5V3AleWvs7jw1sxf09m5U8MV9QmPEAY2LD3Atw4ldIP2ls++JRSIq3ravR06jLN3nwDLC5F2DF\/dB3qjH2pqoluBpOkoSzZZ0z\/sCP\/WIMVPMPhTWPGtVHbW8xeh4pxfaYu\/n11K9MlWUWq6ULOfn84\/O97E1KZ\/mD3bm6cbD9B\/vVhqsGXHx983+NLxrHtsDvXxjVj3s+gYPfXVyQqd5V7h2AprURW8JGGDoXHt4hvZaqKPnUHElrow75+Da4+i9Gj5aCtZkjehjTWYRGwOQthYfkmHP4LXkH10VcR7+mMmlZdRR\/PJXHPtpJ75b1+eLhPpVfc9rb1+gNVPQLRdNuxhTtR3421nces8bogvvnBiNxNOzgupv0+aNGt9\/zCXDLf41tkiCqLPnkKsOca0zP0LiTMb\/PhufA5GeUElpcD82vg2lHr\/gHkpiRyPqE9XRt2LVmrQlQA1itmoU\/H+LtTUd4aXh7hrQv38C6cqnTDLo9YDzA+MJyZj+cPWCs3JaWCHe9b1RPHd9ujEvwuXwN7Pnx81mwa4Fdl+yw7NL2MZPWWJTizvQL1LZaeSckmPGpu5lMn0r\/84T7yAR\/m\/7P+KbfvN\/FyeSO\/GwscFN8XYP8bOMPa8cyIymc2mMsuP7ABmOeGW21e36jXEsuXx3+iuEth0tyuBIPn3SxNMnpOTyxIp58s+b\/7oqmSejlN2SXyjpnNBpnn4OV44zR+A3bQ58pxnia3AtGtZa9in8uR7fAl08Yje+R3R0fv3A6meCvNOFdLi6NCUaCKPp690o4\/CMc\/wV8g2DiT1C3OfSfAeEx4Gdb9KWcvTVyzDkcv3Acq7ZiUtW8T3wN893vyUxftYf7ujfj4QEtMXnCxHwFveP8gmD8d8Y8XidijVH45jx4pb3xfziyJ1x9y6VtIAWKfqEqcGAd\/DgLLiQbKw5GuHEBLOEULksSSikTMBsYC\/gD64GJWuuzJewbDswHooFIYLTW+n2nBFawNObKscbrD+6Ehu3g9y+N99JPQHhnY6qLBtdcPKaC8i35LNy9kAfaP8CjXR6tdPjCc+TkW5j99R9s2JfMgnu7EBNVjrm2XM23ljHyu8BTB+HUbqODRcZpY9vyUca08ZE9jZX8in+h2rsKvpoKbW6G+9cYizuJaseVJYnpwDCgO5ACvA28B9xUwr5WjCTyMvCR0yNr3g+6\/tUYyNTgGmNsQmQP470+Uxx6KS\/lRcPAhvh4cpdFUW4HT1\/g4Q92clVYEF892peQwCr2+Zp8jIWlwovMEXbjS0YPqqNbjU4Yty2GDncYX6QAPptoDPCUVeKqNVcmiQnAC1rrwwBKqaeBg0qpKK11QtEdtdYngf\/Z9rM4PbIjP8OOt42fzx8xiuYFs306iNaaF395kQc7PMioNqMcem7hPlprPvr1OHPX7WfakDaMiomoPm1MYa2NR9exF7e1vMHovZe0E3o9KgmiBnDJqBalVAhGtdGOgm1a60NAOtDRAeefoJSKVUrFnjlzpnwHF2+DKKh6OvJzZcMqHiM3NLuBsIAwh55XuE9aVj6Tl8fx3tajrJjYkzu7RVafBFEabz9IPWb8vGOpw\/9OhOdx1dDHgsrK4t1UUou8V2Fa68Va6xitdUxYWDlvwolxRmIo+EZU0EaRGFfZsAq9sPUF4pLj6NWkl1QzVRPbj5xj6GsbaRwSwGd\/60XLBkHuDsn5XPSFSngWV1U3XbA9F5+JLhSjNOE+xbu5gpEoHFCMNlvNmJSJ0deMpmlQDVj6swYwW6y8\/v1BPth+jJdv70j\/tg3cHZLrXOkLlVQ7VVsuSRJa61Sl1DGgCxAPoJRqgVGK2O2KGNxhfvx8ImpHMKLVCHeHIhzgxPksHv8oHn8fE2sf6UOD4GowM2t5OPELlfBcrmy4XgxMU0r9gNG7aQ6wrnijdQGlVMFfoAJ8bK\/NWmuzK4KtDLPVTJ4lj7Htx+JvqmE3kmrqqz0neW71Xsb3bcH4vi3w8oSxD0K4gCuTxGygDvAr4AdsAO4DUErdCyzSWhet2M0u8vPbtsfzwExXBFsZnx\/8nMSMRB7r8pi7Q\/FcP8yCn2bbt+9MO9bLuG66McDRwbLyzLz45T62HkphyZhudIoIdfg1hPBkLksSWmsLMNX2KP7ecmB5sW1V7qua2WrmTNYZbmt1G2arxxd43Kv\/DKfc1B1pX1I6j3wYR6eIUL58tC9BfjJBgah5ZGJ3B9p5eidvxL+Bl\/LC1+Tr7nBEBWmtWbr5CPct2cYjA1rx31HRkiBEjSX\/8x3AYrXwW8pvdGvUjZiGl82PJaqQlIxcnvpkNymZeXw2uRfN6tVyd0hCuJWUJBwgKTOJ5b8vR2td\/QdTVWOb\/jzL0Nc20qZRbT6Z1FMShBBISaJSLFYL64+uZ0jUEOb0m+PucEQF5Zmt\/GfDflbvTOK\/o6Lp3bK+u0MSwmNISaISciw5xJ+OJ8+a5+5QRAUdTcnkjoVbOJicwVeP9ZUEIUQxkiQqwKqtLN27FIAZ3WfgZ\/Jzc0SiIlbFnWDE\/C3c1qUpb42JoW4t6WwgRHFS3VRBJmVCIe0PVdGFnHyeW\/0bexLTWP5gd65uLOsgCFEaKUmU02txr3H8wnHub3c\/gT6B7g5HlFP88VRueX0T\/j4mvni4jyQIIcogJYlyim4QTf0AqbeuaqxWzaKfD7Nk02FeGt6eIe0buzskIaoESRJ2ei3uNWIaxtCvqUxmVtUkp+fwxIp48s2a1Q\/3ITw0wN0hCVFlSJIog9YagJtb3EzDwIZujkaU13e\/JzN91R7u696Mhwe0xCQT8wlRLpIkyvDuvnfxUl6Mvma0u0MR5ZCTb2H213+wYV8y8+\/tQreouu4OSYgqSZJEKbTW5FpyGdFqhPRiqmIOnr7Awx\/s5KqwIL56tC8hgbIaoBAVVSOSxCsbDvDqd3\/asecHMH0tAN61d2OqdZjcU8Mv2+uxga2YMqi1Y4MUlaa15qNfjzN33X6eHtyGO7tFyDQpQlRSjUgSUwa1tu+mPjME\/c9UzmafpV7ATeSYc6SbaxWRlpXP9FW7SUjJYsXEnjVjzWkhXKBGJIn58fNZsGtB2Ts2j4R3O5a520OdHmJy9GQHRCYc4deEczz+UTw3tmvIK3dG4+9jcndIQlQbNSJJTI6eXOpN\/a9fTGf72W9QXpbCbdpqonvYTSy5ZZarQhQVYLZYef37g3yw\/Rhzbu\/AgLbS+0wIR6sRSeJKfv+9O4StK7ZVERfflR9bnSbIz5tAX2\/j2c9ELV9v\/H28pK7bzRJTs3n8o534eZtY+0gfGgTLWuJCOEPNSBJXWE\/5VM77+Pp0xSc0FuVlQVtN5KfGkJHhz5JlS8jU\/mThTwb+ZGl\/MvEnHx9q+flQq0jiqFX4bPwcWPCzr4lAP2+CbNuMpGOy7We8X8vPGx+TzJBir6\/2nOS51XsZ37cF4\/u2wEvGPgjhNDUjSVxhPeUms78nKWUgPqE7bFsUeWcHEh4ayHvTSz4m32IlK89CVp6ZzFwzmbkW49m2LSPXTFauhcw8M2czcsk8l1W4X+ExeRayco19M\/MsmJS6NOH4eVPL10goQZcko6LbLiaZoscF+hr7VrebZ1aemRe\/3MfWQyksGdONThGh7g5JiGrPZUlCKWUCZgNjAX9gPTBRa322lP2HAP8BWgCHgCe01usdHddTg9swY1Ue+ald8amznfzUGPy9QnlqcJtSj\/ExeRES4EVIgGP632utyTUbicdIIMUSii3hFGxLTM0jK9dCRp6ZLFuSycw1Xzw+10x2vgU\/b9MlJZugwhJOCaWeoqWbghJQkWq2ID9v\/LxdV832+c5E5q7bT1JqNk1CA7ineySr4k7QKSKULx\/tK2tOO8sVSt2XmRlS9j7XTS\/1C5qoGlTBtBNOv5BSfwfGAEOAFOBtIFBrfVMJ+7YA9gITgBXAHcBioJ3WOuFK14mJidGxsbGXbCurd1NeWjT5Kb3xa\/gVuclD8am3Gd+Q+FL3rwq9m6xWTXa+kVyyci1G6SavINkU3XYxyRQkoYyiCafI8fkW68XSjB3VbJcmqJJLQCVVs32+M5EZq\/aQnW+5ZPt9PSJ5aXgHV\/0KhahRlFI7tNYxl213YZI4CrygtV5ie30VcBBoXvzGr5R6Hhigte5bZNtG4Fut9fNXuk5JScJeUdPXkjD75godWxOYLVay8i3FqtguVq0VTzJGtVuRJFRQ4inys1cJ1Wz7ktLJNVsvu354aACbpw9ww79ciOqvtCThkjK7UioEiAQKKv7RWh9SSqUDHYGEYod0KrqvTZxte0nnn4BR6iAyMvKy9+0fcW0kirLU1BHX3iYvgk1eBPtXvprtzkVb2XbkHKDJy7KSmpVf5jGJqdmlfj7dm9fl44k9Kx2XEOJSrqrYLVjZJa3Y9tQi7xVVu5R925V0cq31YozqKGJiYi4rGtk94lq4zJVu6L1nf09iavZl26UkIYTruarf5QXbc\/GWrlAgvZT97d1XVDNPDW5DQLFR0wE+pit2JhBCOIdLkoTWOhU4BnQp2GZrnA4GdpdwyK6i+9p0tm0X1dzwzuHMuq0D4aEBKIwSxKzbOjC8c7i7QxOixnF176b7udi7aQlQW2s9pIR9rwL2AA8AnwAjgbeoYO8mIYQQV1Zaw7Urh\/nOBr4AfgUSARNwny24e5VSGQU7aq0PAbcBz2JUMT0LjCgrQQghhHAsl5UkXEVKEkIIUX6eUJIQQghRxUiSEEIIUSpJEkIIIUpV7doklFJngKMVPLw+UOKEg8Jt5DPxTPK5eJ7KfibNtNZhxTdWuyRRGUqp2JIaboT7yGfimeRz8TzO+kykukkIIUSpJEkIIYQolSSJSy12dwDiMvKZeCb5XDyPUz4TaZMQQghRKilJCCGEKJUkCSGEEKWSJCGEEKJUkiQApdS\/lFJHlFLpSqnTSqlPlFKXr4MqXE4p5aWU2qKU0kqppu6OpyZTSr2jlMpXSmUUeUx2d1wClFI3KKV+sX0mZ5VS8x11bkkShveAaK11MBCFsUDSR26NSBSYAmS5OwhRaJnWOqjIw2E3I1ExSqnrMdbdmQfUA5pirL\/jEK5a49qjaa3\/KPJSAVZA1sp0M6VUa2AycDuw083hCOGpZgELtdafFNkW56iTS0nCRil1j1IqDcgAHgNmujeimk0p5QW8DTwFpLo3GlHE7Uqpc0qpA0qpuUqpIHcHVJMppWoB1wI5Sqk4W1XTj0oph03PIUnCRmv9gdY6BGiMkSD2uDeiGu8x4JTWepW7AxGFXgfaYkwkNwK4DnjTrRGJOhj38fHAWKAJsB74SikV6ogLyGC6EiilGgCHgUit9Tl3x1PTKKVaAj8CMVrrU0qpKOAIEKG1PuHO2MRFSqneGJ9TkNY6183h1EhKqRCMkva\/tNbP2rYp4Bxwr9b6q8peQ0oSJfMGamFkZeF6fYAwYK9S6iwX61d3S28aj2K1PSu3RlGDaa3TgASgpG\/7DikB1PgkYeti+bCt9ICtm+X\/MH7xf1zpWOE0K4CrgGjbY6ht+43Au+4JSSil7iqowlBKtQL+A6zRWue4NTAxHxinlLpGKeWN0Y6XA2xxxMmld5NhKPCcrREoFaMIfYPW2uzOoGoqrXUWRbq92v7jg9FGkeGeqAQwCZivlPIDTgOfIR08PME8oDbwPeCP0RPwJlspo9KkTUIIIUSpanx1kxBCiNJJkhBCCFEqSRJCCCFKJUlCCCFEqSRJCCGEKJUkCSGEEKWSJCGEEKJUkiSEEEKUSpKEEOWglFqnlHrC3XEI4SqSJIQon844eQEkpVSSUsqilGpcZJu3UipLKTXImdcWojhJEkLYSSkVjjE7bbyTr9EYOADcUeStdkAAEOusawtREkkSQtivM5CgtT4PhbOixiulLiil\/lBKDS+6s221w9+UUulKqZVKqXlKqQ\/LuEY3IAVjhtU7i2yPAQ4VXFsIV5EkIYT9umCralJKTcBYW3i81ro2MAX4UCkVaXv\/Adv7D2CsHrYReJSySyHdMEoLq4AYpVREse1CuJQkCSHs1xmIU0rVxkgAf9Va\/wqgtf4aOAN0UUoFAi8Df9Na\/6K1tgBvAT7ATqVUV6XUZqXUz0qp75VSLYpcoxsQa1sR8QdglG17DPCrK\/6RQhQlSUII+xU0WvcELFrrHwresC0ZWQ9IBK4HzFrrL4scW9\/2HA8kAUO01v0w1gJ4vsh+RZPBCuBOpZQv0AEpSQg3kCQhhB2UUnWAZhhJogFQvG3gVozVwPbY3k8t9v7tQJLW+rTW+qTW+oJtex5gtl2jJUbVVEEy+AzoBIzAWCAsDiFcTJKEEPbpDJzWWicB24EopVQ\/pZRJKTUAWAg8aVvKcw\/QUik1QCnlo5QaAfyTYu0RtpUQZ2OUJsCoajqptU4EsDVSfwf8C9hfJLEI4TKSJISwT+H4CK31AeBBYCmQjtET6VGt9Tu293cALwArMaqW+gKbgW0FJ7NVIa0EXtJa\/2bbXFLj9McY631LVZNwC1m+VAgns1VVHQV6a633KKVMGDf\/b7TWb7k3OiGuTJKEEA6mlOoGZAB\/YJQCFgMntNb3296\/C6O3U0HpYI\/W+hF3xCpEWSRJCOFgSqmxGG0NtTGqmz4AZtnaK4SoUiRJCCGEKJU0XAshhCiVJAkhhBClkiQhhBCiVJIkhBBClEqShBBCiFJJkhBCCFEqSRJCCCFK9f8JBg\/uuIsSUgAAAABJRU5ErkJggg==\" \/><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>$\\Delta$ \u304c\u3044\u305a\u308c\u306e\u5834\u5408\u306b\u304a\u3044\u3066\u3082\u3001\u554f\u984c\u30b5\u30a4\u30ba $N$ \u304c\u5897\u52a0\u3059\u308b\u3054\u3068\u306b MAPE \u306f\u5897\u52a0\u3059\u308b\u50be\u5411\u306b\u3042\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001$\\Delta$ \u306b\u3088\u308b MAPE \u306e\u9055\u3044\u306f\u3042\u307e\u308a\u898b\u3089\u308c\u307e\u305b\u3093\u3002\u307e\u305f\u3001\u30a8\u30e9\u30fc\u30d0\u30fc\u3082\u5927\u304d\u304f\u3001\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3054\u3068\u306b MAPE \u304c\u5927\u304d\u304f\u7570\u306a\u308b\u7d50\u679c\u3068\u306a\u308a\u307e\u3057\u305f\u3002<\/p>\n<p>\u5143\u8ad6\u6587\u3067\u306f $\\Delta$ \u304c\u5927\u304d\u3044\u307b\u3069 MAPE \u304c\u5c0f\u3055\u304f\u306a\u308b\u3068\u3044\u3046\u7d50\u679c\u304c\u793a\u3055\u308c\u3066\u304a\u308a\u3001$\\Delta=1.0$ \u306e MAPE \u306f\u307b\u307c\u30bc\u30ed\u3068\u306a\u3063\u3066\u3044\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4eca\u56de\u5f97\u3089\u308c\u305f\u7d50\u679c\u306f\u305d\u308c\u3068\u306f\u5927\u304d\u304f\u7570\u306a\u308a\u307e\u3059\u3002\u539f\u56e0\u306e 1 \u3064\u3068\u3057\u3066\u3001\u5143\u8ad6\u6587\u3067\u306f D-Wave 2000Q \u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3057\u305f\u304c\u3001D-Wave 2000Q \u306f\u65e2\u306b\u30b5\u30fc\u30d3\u30b9\u304c\u7d42\u4e86\u3057\u3066\u3057\u307e\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u4eca\u56de\u306e\u5b9f\u9a13\u3067\u306f D-Wave Advantage6.3 \u3092\u4f7f\u7528\u3057\u305f\u3053\u3068\u304c\u6319\u3052\u3089\u308c\u307e\u3059\u3002\u305d\u3046\u306f\u8a00\u3063\u3066\u3082\u3001\u7d50\u679c\u306b\u3053\u308c\u307b\u3069\u5927\u304d\u306a\u9055\u3044\u304c\u51fa\u305f\u539f\u56e0\u306f\u4e0d\u660e\u3067\u3059\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%BE%E3%81%A8%E3%82%81\"><\/span>\u307e\u3068\u3081<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u672c\u8a18\u4e8b\u3067\u306f\u3001\u5143\u8ad6\u6587\u306e ADMM \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u307e\u3057\u305f\u3002\u305d\u3057\u3066\u3001\u518d\u73fe\u5b9f\u9a13\u3068\u3057\u3066 $\\Delta = 0.2, 0.6, 1.0$ \u306b\u3064\u3044\u3066 MAPE \u306e $N$ \u4f9d\u5b58\u6027\u3092\u8a55\u4fa1\u3057\u307e\u3057\u305f\u3002<\/p>\n<p>\u5143\u8ad6\u6587\u3068\u306f\u7570\u306a\u308a\u3001\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u306b\u3088\u3063\u3066 MAPE \u304c\u5927\u304d\u304f\u5909\u5316\u3059\u308b\u7d50\u679c\u3068\u306a\u308a\u307e\u3057\u305f\u3002\u307e\u305f\u3001$\\Delta$ \u306b\u3088\u308b\u9055\u3044\u3082\u306f\u3063\u304d\u308a\u3068\u306f\u898b\u3089\u308c\u307e\u305b\u3093\u3067\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2><span class=\"ez-toc-section\" id=\"%E3%81%82%E3%81%A8%E3%81%8C%E3%81%8D\"><\/span>\u3042\u3068\u304c\u304d<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\u5143\u8ad6\u6587\u306e\u7d50\u679c\u304c\u518d\u73fe\u3055\u308c\u305f\u3068\u306f\u8a00\u3044\u96e3\u3044\u7d50\u679c\u3068\u306f\u306a\u308a\u307e\u3057\u305f\u304c\u3001\u62e1\u5f35\u30e9\u30b0\u30e9\u30f3\u30b8\u30e5\u6cd5\u3084 ADMM \u306e\u52c9\u5f37\u306b\u3082\u306a\u308a\u3001\u826f\u3044\u7d4c\u9a13\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u307e\u305f\u3001\u4eca\u56de\u306f QKP \u3068\u3044\u3046\u4e0d\u7b49\u5f0f\u5236\u7d04\u304c 1 \u3064\u3060\u3051\u306e\u554f\u984c\u3092\u6271\u3044\u307e\u3057\u305f\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u4e0d\u7b49\u5f0f\u5236\u7d04\u304c\u542b\u307e\u308c\u308b\u554f\u984c\u3082\u4eca\u56de\u306e\u624b\u6cd5\u3067\u6271\u3048\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u304b\u3081\u3066\u307f\u305f\u3044\u3068\u601d\u3044\u307e\u3057\u305f\u3002<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u89e3\u8aac\u8a18\u4e8b\u300c<a href=\"https:\/\/qard.is.tohoku.ac.jp\/T-Wave\/?p=5782\">\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068ADMM\u306e\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u65b9\u5f0f\u306b\u3088\u308b\u4e0d\u7b49\u5f0f\u5236\u7d04\u3078\u306e\u5bfe\u51e6<\/a>\u300d\u3067\u306f\u3001\u4e0d\u7b49\u5f0f\u5236\u7d04\u4ed8\u304d\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\uff08QA : Quantum Annealing\uff09\u3068 ADMM\uff08Alternating Direction Method of Multipliers\uff09\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u624b\u6cd5\u3092\u63d0\u6848\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u305d\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u3001\u5143\u8ad6\u6587\u306e\u518d\u73fe\u5b9f\u9a13\u3092\u884c\u3044\u307e\u3059\u3002<\/p>\n","protected":false},"author":12,"featured_media":8199,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[10,13,85,94],"class_list":["post-7362","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-hands-on","tag-d-wave","tag-d-wave-advantage","tag-85","tag-94"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ 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property=\"og:description\" content=\"\u89e3\u8aac\u8a18\u4e8b\u300c\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\u3068ADMM\u306e\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u65b9\u5f0f\u306b\u3088\u308b\u4e0d\u7b49\u5f0f\u5236\u7d04\u3078\u306e\u5bfe\u51e6\u300d\u3067\u306f\u3001\u4e0d\u7b49\u5f0f\u5236\u7d04\u4ed8\u304d\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u305f\u3081\u306b\u3001\u91cf\u5b50\u30a2\u30cb\u30fc\u30ea\u30f3\u30b0\uff08QA : Quantum Annealing\uff09\u3068 ADMM\uff08Alternating Direction Method of Multipliers\uff09\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u624b\u6cd5\u3092\u63d0\u6848\u3057\u305f\u8ad6\u6587\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u672c\u8a18\u4e8b\u3067\u306f\u3001\u305d\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3057\u3001\u5143\u8ad6\u6587\u306e\u518d\u73fe\u5b9f\u9a13\u3092\u884c\u3044\u307e\u3059\u3002\" \/>\n<meta property=\"og:url\" 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