支持向量机算法很游泳啊

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svm算法详细介绍了程序的具体实现过程,应用较为广泛
SVM.rar
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<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/6250abd774bc5c01056fdec4/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6250abd774bc5c01056fdec4/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Sequen<span class="_ _0"></span>tial<span class="_ _1"> </span>Minimal<span class="_ _1"> </span>Optimization<span class="_ _1"> </span>for<span class="_ _1"> </span>SVM</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls0 ws0">Con<span class="_ _0"></span>ten<span class="_ _0"></span>ts</div><div class="t m0 x2 h4 y3 ff3 fs2 fc0 sc0 ls0 ws0">1<span class="_ _2"> </span>In<span class="_ _0"></span>tro<span class="_ _3"></span>duction<span class="_ _4"> </span>to<span class="_ _4"> </span>Supp<span class="_ _3"></span>ort<span class="_ _4"> </span>V<span class="_ _5"></span>ector<span class="_ _4"> </span>Mac<span class="_ _0"></span>hine<span class="_ _4"> </span>(SVM)<span class="_ _6"> </span>2</div><div class="t m0 x3 h4 y4 ff4 fs2 fc0 sc0 ls0 ws0">1.1<span class="_ _7"> </span>Linear<span class="_ _8"> </span>SVM<span class="_ _9"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _b"> </span>2</div><div class="t m0 x3 h4 y5 ff4 fs2 fc0 sc0 ls0 ws0">1.2<span class="_ _7"> </span>The<span class="_ _8"> </span>dual<span class="_ _8"> </span>problem<span class="_"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _b"> </span>3</div><div class="t m0 x3 h4 y6 ff4 fs2 fc0 sc0 ls0 ws0">1.3<span class="_ _7"> </span>Non-linear<span class="_ _8"> </span>SVM<span class="_ _c"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _b"> </span>4</div><div class="t m0 x3 h4 y7 ff4 fs2 fc0 sc0 ls0 ws0">1.4<span class="_ _7"> </span>Imp<span class="_ _3"></span>erfect<span class="_ _8"> </span>separation<span class="_ _d"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _b"> </span>5</div><div class="t m0 x3 h4 y8 ff4 fs2 fc0 sc0 ls0 ws0">1.5<span class="_ _7"> </span>The<span class="_ _8"> </span>KKT<span class="_ _8"> </span>conditions<span class="_ _e"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _b"> </span>6</div><div class="t m0 x3 h4 y9 ff4 fs2 fc0 sc0 ls0 ws0">1.6<span class="_ _7"> </span>Chec<span class="_ _0"></span>king<span class="_ _8"> </span>KKT<span class="_ _8"> </span>condition<span class="_ _8"> </span>without<span class="_ _8"> </span>using<span class="_ _8"> </span>threshold<span class="_ _8"> </span><span class="ff5">b<span class="_ _9"> </span></span>.<span class="_ _a"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _b"> </span>7</div><div class="t m0 x2 h4 ya ff3 fs2 fc0 sc0 ls0 ws0">2<span class="_ _2"> </span>SMO<span class="_ _4"> </span>Algorithm<span class="_ _f"> </span>9</div><div class="t m0 x3 h4 yb ff4 fs2 fc0 sc0 ls0 ws0">2.1<span class="_ _7"> </span>Optimize<span class="_ _8"> </span>t<span class="_ _0"></span>wo<span class="_ _8"> </span><span class="ff5">&#945;</span></div><div class="t m0 x4 h5 yc ff6 fs3 fc0 sc0 ls0 ws0">i</div><div class="t m0 x5 h4 yb ff4 fs2 fc0 sc0 ls0 ws0">&#8217;s<span class="_ _7"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _b"> </span>9</div><div class="t m0 x3 h4 yd ff4 fs2 fc0 sc0 ls0 ws0">2.2<span class="_ _7"> </span>SMO<span class="_ _8"> </span>Algorithm:<span class="_ _9"> </span>Up<span class="_ _3"></span>dating<span class="_ _8"> </span>after<span class="_ _8"> </span>a<span class="_ _8"> </span>successful<span class="_ _8"> </span>optimization<span class="_ _8"> </span>step<span class="_ _10"> </span>.<span class="_ _11"> </span>13</div><div class="t m0 x3 h4 ye ff4 fs2 fc0 sc0 ls0 ws0">2.3<span class="_ _7"> </span>SMO<span class="_ _8"> </span>Algorithm:<span class="_ _9"> </span>Pick<span class="_ _8"> </span>t<span class="_ _0"></span>w<span class="_ _0"></span>o<span class="_ _8"> </span><span class="ff5">&#945;</span></div><div class="t m0 x6 h5 yf ff6 fs3 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7 h4 ye ff4 fs2 fc0 sc0 ls0 ws0">&#8217;s<span class="_ _8"> </span>for<span class="_ _8"> </span>optimization<span class="_ _9"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _11"> </span>14</div><div class="t m0 x2 h4 y10 ff3 fs2 fc0 sc0 ls0 ws0">3<span class="_ _2"> </span>C</div><div class="t m0 x8 h6 y11 ff7 fs4 fc0 sc0 ls0 ws0">+<span class="_ _5"></span>+</div><div class="t m0 x9 h4 y10 ff3 fs2 fc0 sc0 ls0 ws0">Implemen<span class="_ _0"></span>tation<span class="_ _12"> </span>15</div><div class="t m0 x3 h4 y12 ff4 fs2 fc0 sc0 ls0 ws0">3.1<span class="_ _7"> </span>The<span class="_ _8"> </span><span class="ff8">main<span class="_ _8"> </span></span>routine<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>15</div><div class="t m0 x3 h4 y13 ff4 fs2 fc0 sc0 ls0 ws0">3.2<span class="_ _7"> </span>The<span class="_ _8"> </span><span class="ff8">examineExample<span class="_ _8"> </span></span>routine<span class="_ _13"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>18</div><div class="t m0 x3 h4 y14 ff4 fs2 fc0 sc0 ls0 ws0">3.3<span class="_ _7"> </span>The<span class="_ _8"> </span><span class="ff8">takeStep<span class="_ _8"> </span></span>routine<span class="_ _10"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>20</div><div class="t m0 x3 h4 y15 ff4 fs2 fc0 sc0 ls0 ws0">3.4<span class="_ _7"> </span>Ev<span class="_ _0"></span>aluating<span class="_ _8"> </span>classi&#64257;cation<span class="_ _8"> </span>function<span class="_ _d"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>24</div><div class="t m0 x3 h4 y16 ff4 fs2 fc0 sc0 ls0 ws0">3.5<span class="_ _7"> </span>F<span class="_ _5"></span>unctions<span class="_ _8"> </span>to<span class="_ _8"> </span>compute<span class="_ _8"> </span>dot<span class="_ _8"> </span>pro<span class="_ _3"></span>duct<span class="_ _14"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>26</div><div class="t m0 x3 h4 y17 ff4 fs2 fc0 sc0 ls0 ws0">3.6<span class="_ _7"> </span>Kernel<span class="_ _8"> </span>functions<span class="_ _2"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>28</div><div class="t m0 x3 h4 y18 ff4 fs2 fc0 sc0 ls0 ws0">3.7<span class="_ _7"> </span>Input<span class="_ _8"> </span>and<span class="_ _8"> </span>output<span class="_ _a"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>29</div><div class="t m0 xa h4 y19 ff4 fs2 fc0 sc0 ls0 ws0">3.7.1<span class="_ _15"> </span>Get<span class="_ _8"> </span>parameters<span class="_ _8"> </span>b<span class="_ _0"></span>y<span class="_ _8"> </span>command<span class="_ _8"> </span>line<span class="_ _9"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _11"> </span>29</div><div class="t m0 xa h4 y1a ff4 fs2 fc0 sc0 ls0 ws0">3.7.2<span class="_ _15"> </span>Read<span class="_ _8"> </span>in<span class="_ _8"> </span>data<span class="_ _16"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _11"> </span>31</div><div class="t m0 xa h4 y1b ff4 fs2 fc0 sc0 ls0 ws0">3.7.3<span class="_ _15"> </span>Sa<span class="_ _0"></span>ving<span class="_ _8"> </span>and<span class="_ _8"> </span>loading<span class="_ _8"> </span>mo<span class="_ _3"></span>del<span class="_ _8"> </span>parameters<span class="_ _17"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>34</div><div class="t m0 x3 h4 y1c ff4 fs2 fc0 sc0 ls0 ws0">3.8<span class="_ _7"> </span>Compute<span class="_ _8"> </span>error<span class="_ _8"> </span>rate<span class="_ _4"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>36</div><div class="t m0 x3 h4 y1d ff4 fs2 fc0 sc0 ls0 ws0">3.9<span class="_ _7"> </span>Multiclass<span class="_ _e"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _11"> </span>37</div><div class="t m0 x3 h4 y1e ff4 fs2 fc0 sc0 ls0 ws0">3.10<span class="_ _1"> </span>Mak<span class="_ _0"></span>e&#64257;les<span class="_ _c"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _1"> </span>.<span class="_ _a"> </span>.<span class="_ _11"> </span>40</div><div class="t m0 x2 h4 y1f ff3 fs2 fc0 sc0 ls0 ws0">A<span class="_ _d"> </span>The<span class="_ _4"> </span>weigh<span class="_ _0"></span>t<span class="_ _4"> </span>v<span class="_ _0"></span>ectors<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>parallel<span class="_ _4"> </span>supp<span class="_ _3"></span>orting<span class="_ _4"> </span>planes<span class="_ _18"> </span>41</div><div class="t m0 x2 h4 y20 ff3 fs2 fc0 sc0 ls0 ws0">B<span class="_ _19"> </span>The<span class="_ _4"> </span>ob<span class="_ _3"></span>jective<span class="_ _4"> </span>function<span class="_ _4"> </span>of<span class="_ _4"> </span>the<span class="_ _4"> </span>dual<span class="_ _4"> </span>problem<span class="_ _1a"> </span>42</div><div class="t m0 xb h4 y21 ff4 fs2 fc0 sc0 ls0 ws0">1</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m1"></div></a><a class="l" rel='nofollow' onclick='return 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