{"id":3099,"date":"2025-08-12T09:01:08","date_gmt":"2025-08-12T01:01:08","guid":{"rendered":"https:\/\/www.leexinghai.com\/aic\/?p=3099"},"modified":"2025-08-17T10:41:08","modified_gmt":"2025-08-17T02:41:08","slug":"2-7-2-kkt%e6%9d%a1%e4%bb%b6%e5%88%9d%e5%ad%a6%e7%90%86%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/www.leexinghai.com\/aic\/2-7-2-kkt%e6%9d%a1%e4%bb%b6%e5%88%9d%e5%ad%a6%e7%90%86%e8%a7%a3\/","title":{"rendered":"2.7.2-KKT\u6761\u4ef6\u521d\u5b66\u7406\u89e3"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\ud83d\udfe9 \u4e00\u3001KKT \u6761\u4ef6\u662f\u4ec0\u4e48\uff1f<\/h2>\n\n\n\n<p>KKT \u6761\u4ef6\u662f<strong>\u6c42\u89e3\u5e26\u7ea6\u675f\u4f18\u5316\u95ee\u9898<\/strong>\u7684\u201c\u6700\u4f73\u901a\u7528\u5de5\u5177\u201d\u3002<br>\u5b83\u662f\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\u7684\u6269\u5c55\uff0c\u53ef\u4ee5\u5904\u7406\u4e0d\u7b49\u5f0f\u7ea6\u675f\u3002<\/p>\n\n\n\n<p>\u7528\u5b66\u8fc7\u7684\u5185\u5bb9\u7406\u89e3\uff1a\u82e5f(\u03c9*)=\u03b8\uff08\u03b1*,\u03b2*)\uff0c\u5219\u901a\u8fc7\u4e0a\u4e00\u7bc7\u7684\u5b9a\u7406\u4e00\u63a8\u51fa\uff1a\u5bf9\u4e8e\u6240\u6709\u7684i=1~k\uff0c\u8981\u4e48\u03b1<sub>i<\/sub>=0\uff0c\u8981\u4e48g<sub>i<\/sub>(\u03c9*)=0\u3002\u8fd9\u5c31\u662fKKT\u6761\u4ef6<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe6 \u4e8c\u3001\u590d\u4e60\u539f\u95ee\u9898\u957f\u4ec0\u4e48\u6837\uff1f<\/h2>\n\n\n\n<p>\u8fd8\u8bb0\u5f97 SVM \u7684\u539f\u95ee\u9898\u662f\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u6700\u5c0f\u5316<\/strong>\uff1a<\/p>\n<\/blockquote>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"248\" height=\"88\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-20.png\" alt=\"\" class=\"wp-image-3102\"\/><\/figure>\n<\/div>\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u7ea6\u675f\u6761\u4ef6<\/strong>\uff08\u5bf9\u6bcf\u4e2a\u6837\u672c i\uff09\uff1a<\/p>\n\n\n\n<p>y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22651<\/p>\n<\/blockquote>\n\n\n\n<p>\u6211\u4eec\u8bb0\u8fd9\u4e2a\u7ea6\u675f\u4e3a\uff1a g<sub>i<\/sub>(\u03c9,b)=1\u2212y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22640<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe5 \u4e09\u3001KKT \u6761\u4ef6\u7684\u56db\u5927\u8981\u70b9<\/h2>\n\n\n\n<p>KKT \u6761\u4ef6\u5206\u56db\u4e2a\u90e8\u5206\uff0c\u9002\u7528\u4e8e\u6700\u5c0f\u5316\u95ee\u9898\uff1a<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">1\ufe0f\u20e3 \u539f\u59cb\u53ef\u884c\u6027\uff08Primal Feasibility\uff09\uff1a<\/h3>\n\n\n\n<p>\u5fc5\u987b\u6ee1\u8db3\u539f\u95ee\u9898\u7684\u7ea6\u675f\uff1a y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22651\u21d2g<sub>i<\/sub>(\u03c9,b)\u22640<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2\ufe0f\u20e3 \u5bf9\u5076\u53ef\u884c\u6027\uff08Dual Feasibility\uff09\uff1a<\/h3>\n\n\n\n<p>\u62c9\u683c\u6717\u65e5\u4e58\u5b50 \u03b1<sub>i<\/sub> > 0\uff08\u4e0d\u80fd\u4e3a\u8d1f\uff09<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3\ufe0f\u20e3 \u4e92\u8865\u677e\u5f1b\u6761\u4ef6\uff08Complementary Slackness\uff09\uff1a<\/h3>\n\n\n\n<p>\u8fd9\u662f SVM \u4e2d\u6700\u91cd\u8981\u7684\u4e00\u6761\uff1a \u03b1<sub>i<\/sub>\u22c5g<sub>i<\/sub>(\u03c9,b)=0<\/p>\n\n\n\n<p>\u4e5f\u5c31\u662f\u8bf4\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5982\u679c\u67d0\u4e2a\u70b9\u4e0d\u5728\u8fb9\u754c\u4e0a\uff08\u5206\u7c7b\u8fb9\u754c\u4e4b\u5916\uff09\uff0c\u90a3\u4e48\u5b83\u7684 \u03b1<sub>i<\/sub>= 0\uff08\u4e0d\u662f\u652f\u6301\u5411\u91cf\uff09<\/li>\n\n\n\n<li>\u5982\u679c\u67d0\u4e2a\u70b9\u5728\u201c\u521a\u597d\u8fb9\u754c\u4e0a\u201d\uff0c\u5373 g<sub>i<\/sub>(\u00b7)= 0$\uff0c\u90a3\u4e48\u5b83\u7684 \u03b1<sub>i<\/sub> > 0\uff08\u662f\u652f\u6301\u5411\u91cf\uff09<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u5c31\u662f<strong>\u652f\u6301\u5411\u91cf<\/strong>\u540d\u5b57\u7684\u6765\u6e90\uff01<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">4\ufe0f\u20e3 \u68af\u5ea6\u96f6\u6761\u4ef6\uff08Stationarity\uff09\uff1a<\/h3>\n\n\n\n<p>\u8fd9\u662f\u8bf4\u539f\u51fd\u6570 + \u62c9\u683c\u6717\u65e5\u9879\u5bf9\u53d8\u91cf\u7684\u5bfc\u6570\u8981\u4e3a 0\uff1a <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"657\" height=\"135\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-19.png\" alt=\"\" class=\"wp-image-3101\" srcset=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-19.png 657w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-19-300x62.png 300w\" sizes=\"auto, (max-width: 657px) 100vw, 657px\" \/><\/figure>\n<\/div>\n\n\n<p>\u8ba1\u7b97\u5bfc\u6570\u4f1a\u53d1\u73b0\uff1a <\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"234\" height=\"87\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-18.png\" alt=\"\" class=\"wp-image-3100\"\/><\/figure>\n<\/div>\n\n\n<p>\u8fd9\u8bf4\u660e\u6743\u91cd \u03c9 \u53ef\u4ee5\u7531\u652f\u6301\u5411\u91cf\u52a0\u6743\u7ec4\u6210\uff01\uff08\u8fd9\u4e5f\u662f SVM \u53ea\u4f9d\u8d56\u652f\u6301\u5411\u91cf\u7684\u6839\u672c\u539f\u56e0\uff09<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe8 \u56db\u3001KKT \u6761\u4ef6\u7684\u4f5c\u7528\u662f\uff1f<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u4f5c\u7528<\/th><th>\u8bf4\u660e<\/th><\/tr><\/thead><tbody><tr><td>\u2705 \u5224\u65ad\u6700\u4f18<\/td><td>\u6ee1\u8db3 KKT \u6761\u4ef6\u5c31\u8bf4\u660e\u627e\u5230\u4e86\u6700\u4f18\u89e3\uff08\u5bf9\u4e8e\u51f8\u95ee\u9898\uff0c\u5982 SVM\uff09<\/td><\/tr><tr><td>\u2705 \u627e\u652f\u6301\u5411\u91cf<\/td><td>\u54ea\u4e9b\u70b9\u662f\u652f\u6301\u5411\u91cf\uff0c\u76f4\u63a5\u770b\u54ea\u51e0\u4e2a \u03b1<sub>i<\/sub> > 0<\/td><\/tr><tr><td>\u2705 \u6784\u5efa\u5bf9\u5076\u95ee\u9898<\/td><td>\u63a8\u5bfc\u5bf9\u5076\u5f62\u5f0f\u7684\u57fa\u7840<\/td><\/tr><tr><td>\u2705 \u6838\u51fd\u6570\u901a\u9053<\/td><td>\u5bf9\u5076\u95ee\u9898\u53ea\u51fa\u73b0 \u03b1 \u548c\u70b9\u79ef \u2192 \u53ef\u4ee5\u7528\u6838\u51fd\u6570\u4ee3\u66ff<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udccc \u603b\u7ed3\u4e00\u53e5\u8bdd\uff1a<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\ud83c\udfaf KKT \u6761\u4ef6\u662f\u652f\u6301\u5411\u91cf\u673a\u6700\u4f18\u89e3\u7684\u5fc5\u8981\u6761\u4ef6\uff0c<br>\u5b83\u63ed\u793a\u4e86\u54ea\u4e9b\u70b9\u662f\u652f\u6301\u5411\u91cf\uff0c\u89e3\u91ca\u4e86 \u03c9 \u600e\u4e48\u7531 \u03b1 \u51b3\u5b9a\uff0c<br>\u5e76\u4e14\u5b83\u8ba9\u6211\u4eec\u80fd\u628a\u539f\u95ee\u9898\u5b8c\u7f8e\u8f6c\u5316\u4e3a\u5bf9\u5076\u95ee\u9898\u3002<\/p>\n<\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udfe9 \u4e00\u3001KKT \u6761\u4ef6\u662f\u4ec0\u4e48\uff1f KKT \u6761\u4ef6\u662f\u6c42\u89e3\u5e26\u7ea6\u675f\u4f18\u5316\u95ee\u9898\u7684\u201c\u6700\u4f73\u901a\u7528\u5de5\u5177\u201d\u3002\u5b83\u662f\u62c9\u683c\u6717\u65e5\u4e58\u5b50\u6cd5\u7684\u6269\u5c55\uff0c\u53ef [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3045,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[63],"tags":[],"class_list":["post-3099","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mlsh"],"_links":{"self":[{"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/posts\/3099","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/comments?post=3099"}],"version-history":[{"count":3,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/posts\/3099\/revisions"}],"predecessor-version":[{"id":3179,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/posts\/3099\/revisions\/3179"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/media\/3045"}],"wp:attachment":[{"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/media?parent=3099"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/categories?post=3099"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.leexinghai.com\/aic\/wp-json\/wp\/v2\/tags?post=3099"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}