{"id":41917,"date":"2025-06-05T15:48:22","date_gmt":"2025-06-05T07:48:22","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/41917.html"},"modified":"2025-06-05T15:48:22","modified_gmt":"2025-06-05T07:48:22","slug":"%e4%bd%bf%e7%94%a8osqp%e6%b1%82%e8%a7%a3%e7%ae%80%e5%8d%95%e4%ba%8c%e6%ac%a1%e8%a7%84%e5%88%92%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/41917.html","title":{"rendered":"\u4f7f\u7528osqp\u6c42\u89e3\u7b80\u5355\u4e8c\u6b21\u89c4\u5212\u95ee\u9898"},"content":{"rendered":"<\/p>\n<h4>\u6587\u7ae0\u76ee\u5f55<\/h4>\n<ul>\n<li>\u4e00\u3001\u95ee\u9898\u63cf\u8ff0<\/li>\n<li>\u4e8c\u3001\u6570\u5b66\u63a8\u5bfc<\/li>\n<li>\n<ul>\n<li>1. \u76ee\u6807\u51fd\u6570\u5904\u7406<\/li>\n<li>2. \u7ea6\u675f\u6761\u4ef6\u5904\u7406<\/li>\n<\/ul>\n<\/li>\n<li>\u4e09\u3001\u4ee3\u7801\u7f16\u5199<\/li>\n<\/ul>\n<h2>\u4e00\u3001\u95ee\u9898\u63cf\u8ff0<\/h2>\n<p>\u5df2\u77e5&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          m <\/p>\n<p>          i <\/p>\n<p>          n <\/p>\n<p>          ( <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>          \u2212 <\/p>\n<p>          1 <\/p>\n<p>           ) <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>          ( <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>          \u2212 <\/p>\n<p>          2 <\/p>\n<p>           ) <\/p>\n<p>           2 <\/p>\n<p>          s <\/p>\n<p>          . <\/p>\n<p>          t <\/p>\n<p>          . <\/p>\n<p>          \u00a0\u00a0 <\/p>\n<p>          0 <\/p>\n<p>          \u2a7d <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>          \u2a7d <\/p>\n<p>          1.5 <\/p>\n<p>          , <\/p>\n<p>          \u00a0\u00a0 <\/p>\n<p>          1 <\/p>\n<p>          \u2a7d <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>          \u2a7d <\/p>\n<p>          2.5 <\/p>\n<p>         min(x_1-1)^2&#043;(x_2-2)^2 \\\\qquad s.t. \\\\ \\\\ 0 \\\\leqslant x_1 \\\\leqslant 1.5,\\\\ \\\\ 1 \\\\leqslant x_2 \\\\leqslant 2.5 <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mord mathnormal\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 2em\"><\/span><span class=\"mord mathnormal\">s<\/span><span class=\"mord\">.<\/span><span class=\"mord mathnormal\">t<\/span><span class=\"mord\">.<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7867em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1.5<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7867em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2.5<\/span><\/span><\/span><\/span><\/span><\/span> \u76ee\u6807\u51fd\u6570\u4e3a\u4e8c\u5143\u4e8c\u6b21\u51fd\u6570&#xff0c;\u53ef\u884c\u57df\u4e3a\u7ebf\u6027\u3001\u51f8\u96c6&#xff0c;\u6b64\u4e3a\u4e8c\u6b21\u89c4\u5212\u95ee\u9898&#xff0c;\u53ef\u5c06\u5176\u8f6c\u6362\u6210\u4e8c\u6b21\u89c4\u5212\u8868\u8fbe\u5f0f\u518d\u8fdb\u884c\u6c42\u89e3\u3002\u76f8\u5173\u6570\u5b66\u6982\u5ff5\u53c2\u8003\u53e6\u4e00\u7bc7&#xff1a; \u6700\u4f18\u5316\u95ee\u9898\u57fa\u7840\u7406\u8bba\u6982\u8ff0\u3002<\/p>\n<h2>\u4e8c\u3001\u6570\u5b66\u63a8\u5bfc<\/h2>\n<h3>1. \u76ee\u6807\u51fd\u6570\u5904\u7406<\/h3>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          f <\/p>\n<p>          ( <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>          , <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>          ) <\/p>\n<p>          &#061; <\/p>\n<p>          ( <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>          \u2212 <\/p>\n<p>          1 <\/p>\n<p>           ) <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>          ( <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>          \u2212 <\/p>\n<p>          2 <\/p>\n<p>           ) <\/p>\n<p>           2 <\/p>\n<p>          &#061; <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>           2 <\/p>\n<p>          \u2212 <\/p>\n<p>          2 <\/p>\n<p>           x <\/p>\n<p>           1 <\/p>\n<p>          \u2212 <\/p>\n<p>          4 <\/p>\n<p>           x <\/p>\n<p>           2 <\/p>\n<p>          &#043; <\/p>\n<p>          C <\/p>\n<p>         f(x_1, x_2)&#061;(x_1-1)^2&#043;(x_2-2)^2 &#061;x_1^2&#043;x_2^2-2x_1-4x_2&#043;C <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span style=\"margin-right: 0.1076em\" class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\">1<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1em;vertical-align: -0.25em\"><\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1141em;vertical-align: -0.25em\"><\/span><span class=\"mord\">2<\/span><span class=\"mclose\"><span class=\"mclose\">)<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1111em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 1.1111em;vertical-align: -0.247em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8641em\"><span class=\"\" style=\"top: -2.453em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.247em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7944em;vertical-align: -0.15em\"><\/span><span class=\"mord\">2<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">\u2212<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.7944em;vertical-align: -0.15em\"><\/span><span class=\"mord\">4<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.0715em\" class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff0c;\u5e38\u6570\u9879\u7528<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          C <\/p>\n<p>         C <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.0715em\" class=\"mord mathnormal\">C<\/span><\/span><\/span><\/span><\/span>\u8868\u793a&#xff1b;<\/p>\n<p>\u4ee4&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>         X <\/p>\n<p>         &#061; <\/p>\n<p>          [ <\/p>\n<p>               x <\/p>\n<p>               1 <\/p>\n<p>               x <\/p>\n<p>               2 <\/p>\n<p>          ] <\/p>\n<p>        X&#061;\\\\left[ \\\\begin{matrix} x_1 \\\\\\\\ x_2 \\\\end{matrix} \\\\right] <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span>&#xff0c;\u5219 <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>              f <\/p>\n<p>              ( <\/p>\n<p>               x <\/p>\n<p>               1 <\/p>\n<p>              , <\/p>\n<p>               x <\/p>\n<p>               2 <\/p>\n<p>              ) <\/p>\n<p>              &#061; <\/p>\n<p>              [ <\/p>\n<p>               x <\/p>\n<p>               1 <\/p>\n<p>              , <\/p>\n<p>               x <\/p>\n<p>               2 <\/p>\n<p>              ] <\/p>\n<p>              [ <\/p>\n<p>               x <\/p>\n<p>               1 <\/p>\n<p>              , <\/p>\n<p>               x <\/p>\n<p>               2 <\/p>\n<p>               ] <\/p>\n<p>               T <\/p>\n<p>              &#043; <\/p>\n<p>              [ <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>              , <\/p>\n<p>              \u2212 <\/p>\n<p>              4 <\/p>\n<p>              ] <\/p>\n<p>              [ <\/p>\n<p>               x <\/p>\n<p>               1 <\/p>\n<p>              , <\/p>\n<p>               x <\/p>\n<p>               2 <\/p>\n<p>               ] <\/p>\n<p>               T <\/p>\n<p>              &#061; <\/p>\n<p>               X <\/p>\n<p>               T <\/p>\n<p>              X <\/p>\n<p>              &#043; <\/p>\n<p>              [ <\/p>\n<p>              \u2212 <\/p>\n<p>              2 <\/p>\n<p>              , <\/p>\n<p>              \u2212 <\/p>\n<p>              4 <\/p>\n<p>              ] <\/p>\n<p>              X <\/p>\n<p>              &#061; <\/p>\n<p>               1 <\/p>\n<p>               2 <\/p>\n<p>               X <\/p>\n<p>               T <\/p>\n<p>               [ <\/p>\n<p>                   2 <\/p>\n<p>                   0 <\/p>\n<p>                   0 <\/p>\n<p>                   2 <\/p>\n<p>               ] <\/p>\n<p>              X <\/p>\n<p>              &#043; <\/p>\n<p>                [ <\/p>\n<p>                     \u2212 <\/p>\n<p>                     2 <\/p>\n<p>                     \u2212 <\/p>\n<p>                     4 <\/p>\n<p>                ] <\/p>\n<p>               T <\/p>\n<p>              X <\/p>\n<p>              &#061; <\/p>\n<p>               1 <\/p>\n<p>               2 <\/p>\n<p>               X <\/p>\n<p>               T <\/p>\n<p>              P <\/p>\n<p>              X <\/p>\n<p>              &#043; <\/p>\n<p>               Q <\/p>\n<p>               T <\/p>\n<p>              X <\/p>\n<p>         \\\\begin{aligned} f(x_1, x_2) &amp;&#061; [x_1, x_2][x_1, x_2]^T&#043;[-2, -4][x_1, x_2]^T \\\\\\\\[2ex] &amp;&#061; X^TX&#043;[-2, -4]X \\\\\\\\[2ex] &amp;&#061;\\\\frac{1}{2} X^T \\\\left[\\\\begin{matrix} 2 &amp;0 \\\\\\\\ 0&amp;2 \\\\end{matrix} \\\\right] X&#043;\\\\left[\\\\begin{matrix} -2 \\\\\\\\ -4 \\\\end{matrix} \\\\right]^TX \\\\\\\\[2ex] &amp;&#061; \\\\frac{1}{2} X^TPX&#043;Q^TX \\\\end{aligned} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 10.3373em;vertical-align: -4.9187em\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 5.4187em\"><span class=\"\" style=\"top: -8.2086em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.1076em\" class=\"mord mathnormal\">f<\/span><span class=\"mopen\">(<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">)<\/span><\/span><\/span><span class=\"\" style=\"top: -5.7952em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: -2.592em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><\/span><\/span><span class=\"\" style=\"top: 0.2514em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 4.9187em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"col-align-l\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 5.4187em\"><span class=\"\" style=\"top: -8.2086em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">4<\/span><span class=\"mclose\">]<\/span><span class=\"mopen\">[<\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose\"><span class=\"mclose\">]<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -5.7952em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mopen\">[<\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\">\u2212<\/span><span class=\"mord\">4<\/span><span class=\"mclose\">]<\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><\/span><\/span><span class=\"\" style=\"top: -2.592em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"minner\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6812em\"><span class=\"\" style=\"top: -3.9029em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><\/span><\/span><span class=\"\" style=\"top: 0.2514em\"><span class=\"pstrut\" style=\"height: 3.6812em\"><\/span><span class=\"mord\"><span class=\"mord\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.3214em\"><span class=\"\" style=\"top: -2.314em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.677em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">PX<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mbin\">&#043;<\/span><span class=\"mspace\" style=\"margin-right: 0.2222em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">Q<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8913em\"><span class=\"\" style=\"top: -3.113em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 4.9187em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p>\u5176\u4e2d&#xff0c;<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          P <\/p>\n<p>          &#061; <\/p>\n<p>           [ <\/p>\n<p>               2 <\/p>\n<p>               0 <\/p>\n<p>               0 <\/p>\n<p>               2 <\/p>\n<p>           ] <\/p>\n<p>          &#xff0c;\u00a0 <\/p>\n<p>          Q <\/p>\n<p>          &#061; <\/p>\n<p>           [ <\/p>\n<p>                \u2212 <\/p>\n<p>                2 <\/p>\n<p>                \u2212 <\/p>\n<p>                4 <\/p>\n<p>           ] <\/p>\n<p>         P&#061;\\\\left[\\\\begin{matrix} 2 &amp;0 \\\\\\\\ 0&amp;2 \\\\end{matrix} \\\\right]&#xff0c;\\\\ Q&#061;\\\\left[\\\\begin{matrix} -2 \\\\\\\\ -4 \\\\end{matrix} \\\\right] <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord cjk_fallback\">&#xff0c;<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">2<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">\u2212<\/span><span class=\"mord\">4<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u2003 \u5173\u4e8e\u4e3a\u4ec0\u4e48\u8981\u5199\u6210 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>           1 <\/p>\n<p>           2 <\/p>\n<p>           X <\/p>\n<p>           T <\/p>\n<p>          P <\/p>\n<p>          X <\/p>\n<p>         \\\\frac{1}{2} X^TPX <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.1901em;vertical-align: -0.345em\"><\/span><span class=\"mord\"><span class=\"mopen nulldelimiter\"><\/span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8451em\"><span class=\"\" style=\"top: -2.655em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -3.23em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em\"><\/span><\/span><span class=\"\" style=\"top: -3.394em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mord\"><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8413em\"><span class=\"\" style=\"top: -3.063em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal mtight\">T<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">PX<\/span><\/span><\/span><\/span><\/span> \u5f62\u5f0f&#xff0c;\u56e0\u4e3a\u6b64\u65f6 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          P <\/p>\n<p>         P <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span><\/span> \u4e3a\u76ee\u6807\u51fd\u6570\u7684\u6d77\u585e\u77e9\u9635&#xff0c;\u5177\u4f53\u53c2\u770b \u6b64\u94fe\u63a5\u3002<\/p>\n<h3>2. \u7ea6\u675f\u6761\u4ef6\u5904\u7406<\/h3>\n<p><span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>               { <\/p>\n<p>                    0 <\/p>\n<p>                    \u2a7d <\/p>\n<p>                     x <\/p>\n<p>                     1 <\/p>\n<p>                    \u2a7d <\/p>\n<p>                    1.5 <\/p>\n<p>                    1 <\/p>\n<p>                    \u2a7d <\/p>\n<p>                     x <\/p>\n<p>                     2 <\/p>\n<p>                    \u2a7d <\/p>\n<p>                    2.5 <\/p>\n<p>              \u27fa <\/p>\n<p>               [ <\/p>\n<p>                   0 <\/p>\n<p>                   1 <\/p>\n<p>               ] <\/p>\n<p>              \u2a7d <\/p>\n<p>               [ <\/p>\n<p>                    x <\/p>\n<p>                    1 <\/p>\n<p>                    x <\/p>\n<p>                    2 <\/p>\n<p>               ] <\/p>\n<p>              \u2a7d <\/p>\n<p>               [ <\/p>\n<p>                   1.5 <\/p>\n<p>                   2.5 <\/p>\n<p>               ] <\/p>\n<p>              \u27fa <\/p>\n<p>               [ <\/p>\n<p>                   0 <\/p>\n<p>                   1 <\/p>\n<p>               ] <\/p>\n<p>              \u2a7d <\/p>\n<p>               [ <\/p>\n<p>                   1 <\/p>\n<p>                   0 <\/p>\n<p>                   0 <\/p>\n<p>                   1 <\/p>\n<p>               ] <\/p>\n<p>              X <\/p>\n<p>              \u2a7d <\/p>\n<p>               [ <\/p>\n<p>                   1.5 <\/p>\n<p>                   2.5 <\/p>\n<p>               ] <\/p>\n<p>         \\\\begin{aligned} \\\\left\\\\{ \\\\begin{array}{} 0 \\\\leqslant x_1 \\\\leqslant 1.5 \\\\\\\\ 1 \\\\leqslant x_2 \\\\leqslant 2.5 \\\\\\\\ \\\\end{array} \\\\right . \\\\quad \\\\Longleftrightarrow \\\\quad \\\\left[\\\\begin{matrix}0 \\\\\\\\1\\\\end{matrix} \\\\right] \\\\leqslant \\\\left[\\\\begin{matrix}x_1 \\\\\\\\x_2\\\\end{matrix} \\\\right] \\\\leqslant \\\\left[\\\\begin{matrix}1.5 \\\\\\\\2.5\\\\end{matrix} \\\\right] \\\\quad \\\\Longleftrightarrow \\\\quad \\\\left[\\\\begin{matrix}0 \\\\\\\\1\\\\end{matrix} \\\\right] \\\\leqslant \\\\left[\\\\begin{matrix}1&amp;0 \\\\\\\\0&amp;1\\\\end{matrix} \\\\right]X \\\\leqslant \\\\left[\\\\begin{matrix}1.5 \\\\\\\\2.5\\\\end{matrix} \\\\right] \\\\end{aligned} <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 2.7em;vertical-align: -1.1em\"><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-r\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.6em\"><span class=\"\" style=\"top: -3.6em\"><span class=\"pstrut\" style=\"height: 3.45em\"><\/span><span class=\"mord\"><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">{<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">1.5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mord\">2.5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><\/span><\/span><span class=\"mclose nulldelimiter\"><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u27fa<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1.5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2.5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">\u27fa<\/span><span class=\"mspace\" style=\"margin-right: 1em\"><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1.5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2.5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.1em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u4ee4<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          L <\/p>\n<p>          B <\/p>\n<p>         &#061; <\/p>\n<p>          [ <\/p>\n<p>              0 <\/p>\n<p>              1 <\/p>\n<p>          ] <\/p>\n<p>         , <\/p>\n<p>         \u00a0 <\/p>\n<p>         A <\/p>\n<p>         &#061; <\/p>\n<p>          [ <\/p>\n<p>              1 <\/p>\n<p>              0 <\/p>\n<p>              0 <\/p>\n<p>              1 <\/p>\n<p>          ] <\/p>\n<p>         , <\/p>\n<p>         \u00a0 <\/p>\n<p>          U <\/p>\n<p>          B <\/p>\n<p>         &#061; <\/p>\n<p>          [ <\/p>\n<p>              1.5 <\/p>\n<p>              2.5 <\/p>\n<p>          ] <\/p>\n<p>        L_B&#061;\\\\left[\\\\begin{matrix}0 \\\\\\\\1\\\\end{matrix} \\\\right],\\\\ A&#061;\\\\left[\\\\begin{matrix}1&amp;0 \\\\\\\\0&amp;1\\\\end{matrix} \\\\right],\\\\ U_B&#061;\\\\left[\\\\begin{matrix}1.5 \\\\\\\\2.5\\\\end{matrix} \\\\right] <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"arraycolsep\" style=\"width: 0.5em\"><\/span><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">0<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.109em\" class=\"mord mathnormal\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 2.4em;vertical-align: -0.95em\"><\/span><span class=\"minner\"><span class=\"mopen delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">[<\/span><\/span><span class=\"mord\"><span class=\"mtable\"><span class=\"col-align-c\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.45em\"><span class=\"\" style=\"top: -3.61em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">1.5<\/span><\/span><\/span><span class=\"\" style=\"top: -2.41em\"><span class=\"pstrut\" style=\"height: 3em\"><\/span><span class=\"mord\"><span class=\"mord\">2.5<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.95em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mclose delimcenter\" style=\"top: 0em\"><span class=\"delimsizing size3\">]<\/span><\/span><\/span><\/span><\/span><\/span><\/span> &#xff0c;\u6574\u7406\u5f97\u7ea6\u675f\u6761\u4ef6\u5982\u4e0b&#xff1a; <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>           L <\/p>\n<p>           B <\/p>\n<p>          \u2a7d <\/p>\n<p>          A <\/p>\n<p>          X <\/p>\n<p>          \u2a7d <\/p>\n<p>           U <\/p>\n<p>           B <\/p>\n<p>         L_B \\\\leqslant AX \\\\leqslant U_B <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.82em;vertical-align: -0.1367em\"><\/span><span class=\"mord mathnormal\">A<\/span><span style=\"margin-right: 0.0785em\" class=\"mord mathnormal\">X<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel amsrm\">\u2a7d<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.109em\" class=\"mord mathnormal\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<h2>\u4e09\u3001\u4ee3\u7801\u7f16\u5199<\/h2>\n<p>\u2003\u2003\u7531\u6b65\u9aa4 \u4e8c\u3001\u6570\u5b66\u63a8\u5bfc \u5f97\u52305\u4e2a\u77e9\u9635&#xff1a;<\/p>\n<ul>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          P <\/p>\n<p>         P <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span style=\"margin-right: 0.1389em\" class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span><\/span> : \u4e8c\u6b21\u578b\u77e9\u9635(\u5b9e\u5bf9\u79f0\u77e9\u9635)&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          Q <\/p>\n<p>         Q <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8778em;vertical-align: -0.1944em\"><\/span><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span><\/span> : \u4e00\u6b21\u9879\u77e9\u9635&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           U <\/p>\n<p>           B <\/p>\n<p>         U_B <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span style=\"margin-right: 0.109em\" class=\"mord mathnormal\">U<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: -0.109em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> : \u4e0a\u8fb9\u754c\u77e9\u9635&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>           L <\/p>\n<p>           B <\/p>\n<p>         L_B <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.8333em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">L<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3283em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span style=\"margin-right: 0.0502em\" class=\"mord mathnormal mtight\">B<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> : \u4e0b\u8fb9\u754c\u77e9\u9635&#xff1b;<\/li>\n<li><span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\">\n<p>          A <\/p>\n<p>         A <\/p>\n<p>     <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em\"><\/span><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/span> : \u8fb9\u754c\u7cfb\u6570\u77e9\u9635&#xff1b;<\/li>\n<\/ul>\n<p>\u2003\u2003\u73b0\u5728\u6839\u636e\u8fd95\u4e2a\u77e9\u9635\u8fdb\u884c\u4ee3\u7801\u7f16\u5199&#xff0c;\u662f\u4f7f\u7528osqp\u8fdb\u884c\u4e8c\u6b21\u578b\u89c4\u5212\u95ee\u9898\u6784\u5efa\u53ca\u6c42\u89e3\u3002<\/p>\n<p>\u4ee3\u7801\u5982\u4e0b&#xff1a;<\/p>\n<p>Eigen<span class=\"token double-colon punctuation\">::<\/span>SparseMatrix<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">double<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">P<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ P&#xff0c; \u4e8c\u6b21\u578b\u77e9\u9635<\/span><br \/>\nEigen<span class=\"token double-colon punctuation\">::<\/span>VectorXd <span class=\"token function\">Q<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>                <span class=\"token comment\">\/\/ Q&#xff0c; \u4e00\u6b21\u9879\u5411\u91cf<\/span><br \/>\nEigen<span class=\"token double-colon punctuation\">::<\/span>SparseMatrix<span class=\"token operator\">&lt;<\/span><span class=\"token keyword\">double<\/span><span class=\"token operator\">&gt;<\/span> <span class=\"token function\">A<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u5355\u4f4d\u9635<\/span><br \/>\nEigen<span class=\"token double-colon punctuation\">::<\/span>VectorXd <span class=\"token function\">lowerBound<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u4e0b\u8fb9\u754c\u5411\u91cf<\/span><br \/>\nEigen<span class=\"token double-colon punctuation\">::<\/span>VectorXd <span class=\"token function\">upperBound<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>       <span class=\"token comment\">\/\/ \u4e0a\u8fb9\u754c\u5411\u91cf<\/span><\/p>\n<p>P<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">;<\/span><br \/>\nP<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">2.0<\/span><span class=\"token punctuation\">;<\/span><br \/>\nstd<span class=\"token double-colon punctuation\">::<\/span>cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[34m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;P:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<br \/>\n            <span class=\"token operator\">&lt;&lt;<\/span> P <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[0m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<span class=\"token punctuation\">;<\/span><\/p>\n<p>A<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">0<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">;<\/span><br \/>\nA<span class=\"token punctuation\">.<\/span><span class=\"token function\">insert<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">1<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">&#061;<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">;<\/span><br \/>\nstd<span class=\"token double-colon punctuation\">::<\/span>cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[34m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;A:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<br \/>\n            <span class=\"token operator\">&lt;&lt;<\/span> A <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[0m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<span class=\"token punctuation\">;<\/span><\/p>\n<p>Q <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token operator\">&#8211;<\/span><span class=\"token number\">4<\/span><span class=\"token punctuation\">;<\/span><br \/>\nstd<span class=\"token double-colon punctuation\">::<\/span>cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[34m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;Q:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<br \/>\n            <span class=\"token operator\">&lt;&lt;<\/span> Q <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[0m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<span class=\"token punctuation\">;<\/span><\/p>\n<p>lowerBound <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token number\">0.0<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">1.0<\/span><span class=\"token punctuation\">;<\/span><br \/>\nupperBound <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token number\">1.5<\/span><span class=\"token punctuation\">,<\/span> <span class=\"token number\">2.5<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ Step 1&#xff1a; \u521b\u5efa\u6c42\u89e3\u5668<\/span><br \/>\nOsqpEigen<span class=\"token double-colon punctuation\">::<\/span>Solver solver<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token comment\">\/\/ Step 2&#xff1a; \u8bbe\u7f6e(\u63d0\u5347\u6c42\u89e3\u901f\u5ea6)<\/span><br \/>\nsolver<span class=\"token punctuation\">.<\/span><span class=\"token function\">settings<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setVerbosity<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">false<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nsolver<span class=\"token punctuation\">.<\/span><span class=\"token function\">settings<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setWarmStart<\/span><span class=\"token punctuation\">(<\/span><span class=\"token boolean\">true<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><\/p>\n<p><span class=\"token comment\">\/\/ Step 3&#xff1a; \u521d\u59cb\u5316(7\u90e8\u5206)<\/span><br \/>\nsolver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setNumberOfVariables<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span>   <span class=\"token comment\">\/\/ \u53d8\u91cf\u6570<\/span><br \/>\nsolver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setNumberOfConstraints<\/span><span class=\"token punctuation\">(<\/span><span class=\"token number\">2<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span> <span class=\"token comment\">\/\/ \u7ea6\u675f\u6570<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setHessianMatrix<\/span><span class=\"token punctuation\">(<\/span>P<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span>  <span class=\"token comment\">\/\/ \u6d77\u585e\u77e9\u9635<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setGradient<\/span><span class=\"token punctuation\">(<\/span>Q<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ Q\u77e9\u9635<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setLinearConstraintsMatrix<\/span><span class=\"token punctuation\">(<\/span>A<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u7ebf\u6027\u7ea6\u675f\u77e9\u9635A<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setLowerBound<\/span><span class=\"token punctuation\">(<\/span>lowerBound<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u4e0b\u8fb9\u754c\u77e9\u9635<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">data<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token operator\">-&gt;<\/span><span class=\"token function\">setUpperBound<\/span><span class=\"token punctuation\">(<\/span>upperBound<span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token comment\">\/\/ \u4e0a\u8fb9\u754c\u77e9\u9635<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span><span class=\"token operator\">!<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">initSolver<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><\/p>\n<p><span class=\"token comment\">\/\/ Step 4&#xff1a;\u6c42\u89e3<\/span><br \/>\nEigen<span class=\"token double-colon punctuation\">::<\/span>VectorXd QPSolution<span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token keyword\">if<\/span> <span class=\"token punctuation\">(<\/span>solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">solveProblem<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span> <span class=\"token operator\">!&#061;<\/span> OsqpEigen<span class=\"token double-colon punctuation\">::<\/span>ErrorExitFlag<span class=\"token double-colon punctuation\">::<\/span>NoError<span class=\"token punctuation\">)<\/span><br \/>\n<span class=\"token punctuation\">{<\/span><br \/>\n    <span class=\"token keyword\">return<\/span><span class=\"token punctuation\">;<\/span><br \/>\n<span class=\"token punctuation\">}<\/span><br \/>\nQPSolution <span class=\"token operator\">&#061;<\/span> solver<span class=\"token punctuation\">.<\/span><span class=\"token function\">getSolution<\/span><span class=\"token punctuation\">(<\/span><span class=\"token punctuation\">)<\/span><span class=\"token punctuation\">;<\/span><br \/>\nstd<span class=\"token double-colon punctuation\">::<\/span>cout <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[1;32m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;QPSolution:&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<br \/>\n            <span class=\"token operator\">&lt;&lt;<\/span> QPSolution <span class=\"token operator\">&lt;&lt;<\/span> <span class=\"token string\">&#034;\\\\033[0m&#034;<\/span> <span class=\"token operator\">&lt;&lt;<\/span> std<span class=\"token double-colon punctuation\">::<\/span>endl<span class=\"token punctuation\">;<\/span><\/p>\n<p>\u8fd0\u884c\u7ed3\u679c\u5982\u4e0b: <img decoding=\"async\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/06\/20250605074821-68414bc54be60.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" width=\"550\" \/> \u53ef\u89c1&#xff0c;\u5f53<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> <\/p>\n<p>          x <\/p>\n<p>          1 <\/p>\n<p>         &#061; <\/p>\n<p>         1 <\/p>\n<p>         , <\/p>\n<p>         \u00a0 <\/p>\n<p>          x <\/p>\n<p>          2 <\/p>\n<p>         &#061; <\/p>\n<p>         2 <\/p>\n<p>        x_1&#061;1,\\\\ x_2&#061;2 <\/p>\n<p>    <\/span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.5806em;vertical-align: -0.15em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">1<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8389em;vertical-align: -0.1944em\"><\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mspace\">\u00a0<\/span><span class=\"mspace\" style=\"margin-right: 0.1667em\"><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.3011em\"><span class=\"\" style=\"top: -2.55em;margin-left: 0em;margin-right: 0.05em\"><span class=\"pstrut\" style=\"height: 2.7em\"><\/span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2<\/span><\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.15em\"><span class=\"\"><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><span class=\"mrel\">&#061;<\/span><span class=\"mspace\" style=\"margin-right: 0.2778em\"><\/span><\/span><span class=\"base\"><span class=\"strut\" style=\"height: 0.6444em\"><\/span><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span> 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