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class="article_intro">min线性化</div><div class="article_content article_contentheight"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/kdoc_html_views-1a98987dfd.css"> <link rel="stylesheet" href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/ck_htmledit_views-044f2cf1dc.css"> <div id="content_views" class="markdown_views prism-atom-one-light"> <svg xmlns="http://www.w3.org/2000/svg" style="display: none;"> <path stroke-linecap="round" d="M5,0 0,2.5 5,5z" id="raphael-marker-block" style="-webkit-tap-highlight-color: rgba(0, 0, 0, 0);"></path> </svg> <p>数学建模过程中，经常会遇到下面的<a href="https://so.csdn.net/so/search?q=%E8%A1%A8%E8%BE%BE%E5%BC%8F&spm=1001.2101.3001.7020" target="_blank" class="hl hl-1" data-report-click="{"spm":"1001.2101.3001.7020","dest":"https://so.csdn.net/so/search?q=%E8%A1%A8%E8%BE%BE%E5%BC%8F&spm=1001.2101.3001.7020","extra":"{\"searchword\":\"表达式\"}"}" data-tit="表达式" data-pretit="表达式">表达式</a>：<br> <span class="katex--display"><span class="katex-display"><span class="katex"><span class="katex-mathml"> x = max ⁡ { y , 0 } x=\max\{y, 0\} </span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.4306em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</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="mop">max</span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right: 0.1667em;"></span><span class="mord">0</span><span class="mclose">}</span></span></span></span></span></span><br> 这是一个非线性表达式，如何将这个表达式转化为线性，进而调用线性规划软件求解呢？通常需要引入一个 0-1 变量 <span class="katex--inline"><span class="katex"><span class="katex-mathml"> δ \delta </span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.6944em;"></span><span class="mord mathnormal" style="margin-right: 0.0379em;">δ</span></span></span></span></span>，一个大常数 M，转化为五个不等式。如下：<br> <span class="katex--display"><span class="katex-display"><span class="katex"><span class="katex-mathml"> x ≤ y + ( 1 − δ ) M x ≥ y − ( 1 − δ ) M x ≤ δ M y ≤ δ M x ≥ 0 <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display"><span class="MathJax MathJax_FullWidth" id="MathJax-Element-1-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>y</mi><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>y</mi><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>δ</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>δ</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-1" style="width: 100%; display: inline-block; min-width: 7.798em;"><span style="display: inline-block; position: relative; width: 100%; height: 0px; font-size: 102%;"><span style="position: absolute; clip: rect(3.749em, 1007.65em, 10.33em, -999.997em); top: -7.287em; left: 0em; width: 100%;"><span class="mrow" id="MathJax-Span-2"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.749em, 1007.65em, 10.33em, -999.997em); top: -7.287em; left: 50%; margin-left: -3.845em;"><span class="mtable" id="MathJax-Span-3" style="padding-left: 0.154em;"><span style="display: inline-block; position: relative; width: 7.495em; height: 0px;"><span style="position: absolute; clip: rect(3.546em, 1000.51em, 9.621em, -999.997em); top: -6.73em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.559em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -6.578em; left: 0em;"><span class="mtd" id="MathJax-Span-4"><span class="mrow" id="MathJax-Span-5"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-6" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -5.262em; left: 0em;"><span class="mtd" id="MathJax-Span-19"><span class="mrow" id="MathJax-Span-20"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-21" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.895em; left: 0em;"><span class="mtd" id="MathJax-Span-34"><span class="mrow" id="MathJax-Span-35"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-36" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.356em, -999.997em); top: -2.579em; left: 0em;"><span class="mtd" id="MathJax-Span-43"><span class="mrow" id="MathJax-Span-44"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.356em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.251em;"><span class="mi" id="MathJax-Span-45" style="font-family: MathJax_Math-italic;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -1.314em; left: 0em;"><span class="mtd" id="MathJax-Span-52"><span class="mrow" id="MathJax-Span-53"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-54" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 6.735em;"></span></span><span style="position: absolute; clip: rect(3.698em, 1006.94em, 10.178em, -999.997em); top: -7.186em; left: 0.559em;"><span style="display: inline-block; position: relative; width: 6.938em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.091em, 1006.94em, 4.407em, -999.997em); top: -6.578em; left: 0em;"><span class="mtd" id="MathJax-Span-7"><span class="mrow" id="MathJax-Span-8"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.091em, 1006.94em, 4.407em, -999.997em); top: -3.997em; left: 50%; margin-left: -3.49em;"><span class="mi" id="MathJax-Span-9"></span><span class="mo" id="MathJax-Span-10" style="font-family: MathJax_Main; padding-left: 0.256em;">≤</span><span class="mi" id="MathJax-Span-11" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-12" style="font-family: MathJax_Main; padding-left: 0.205em;">+</span><span class="mo" id="MathJax-Span-13" style="font-family: MathJax_Main; padding-left: 0.205em;">(</span><span class="mn" id="MathJax-Span-14" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-15" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mi" id="MathJax-Span-16" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">δ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-17" style="font-family: MathJax_Main;">)</span><span class="mi" id="MathJax-Span-18" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.091em, 1006.94em, 4.407em, -999.997em); top: -5.262em; left: 0em;"><span class="mtd" id="MathJax-Span-22"><span class="mrow" id="MathJax-Span-23"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.091em, 1006.94em, 4.407em, -999.997em); top: -3.997em; left: 50%; margin-left: -3.49em;"><span class="mi" id="MathJax-Span-24"></span><span class="mo" id="MathJax-Span-25" style="font-family: MathJax_Main; padding-left: 0.256em;">≥</span><span class="mi" id="MathJax-Span-26" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">y<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-27" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mo" id="MathJax-Span-28" style="font-family: MathJax_Main; padding-left: 0.205em;">(</span><span class="mn" id="MathJax-Span-29" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-30" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mi" id="MathJax-Span-31" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">δ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-32" style="font-family: MathJax_Main;">)</span><span class="mi" id="MathJax-Span-33" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.141em, 1002.79em, 4.305em, -999.997em); top: -3.895em; left: 0em;"><span class="mtd" id="MathJax-Span-37"><span class="mrow" id="MathJax-Span-38"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1002.79em, 4.305em, -999.997em); top: -3.997em; left: 50%; margin-left: -1.415em;"><span class="mi" id="MathJax-Span-39"></span><span class="mo" id="MathJax-Span-40" style="font-family: MathJax_Main; padding-left: 0.256em;">≤</span><span class="mi" id="MathJax-Span-41" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">δ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-42" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.141em, 1002.79em, 4.305em, -999.997em); top: -2.579em; left: 0em;"><span class="mtd" id="MathJax-Span-46"><span class="mrow" id="MathJax-Span-47"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1002.79em, 4.305em, -999.997em); top: -3.997em; left: 50%; margin-left: -1.415em;"><span class="mi" id="MathJax-Span-48"></span><span class="mo" id="MathJax-Span-49" style="font-family: MathJax_Main; padding-left: 0.256em;">≤</span><span class="mi" id="MathJax-Span-50" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">δ<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-51" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.192em, 1001.77em, 4.305em, -999.997em); top: -1.314em; left: 0em;"><span class="mtd" id="MathJax-Span-55"><span class="mrow" id="MathJax-Span-56"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.192em, 1001.77em, 4.305em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.909em;"><span class="mi" id="MathJax-Span-57"></span><span class="mo" id="MathJax-Span-58" style="font-family: MathJax_Main; padding-left: 0.256em;">≥</span><span class="mn" id="MathJax-Span-59" style="font-family: MathJax_Main; padding-left: 0.256em;">0</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 7.191em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 7.292em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 7.292em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.992em; border-left: 0px solid; width: 0px; height: 6.56em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>y</mi><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>y</mi><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>δ</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>δ</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>y</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>δ</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mn>0</mn></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-1">\begin{aligned} x&\leq y +(1-\delta)M\\ x&\geq y-(1-\delta)M\\ x&\leq \delta M\\ y&\leq \delta M\\ x&\geq 0 \end{aligned}</script> </span><span class="katex-html"><span class="base"><span class="strut" style="height: 7.5em; vertical-align: -3.5em;"></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: 4em;"><span class="" style="top: -6.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -4.66em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -3.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -1.66em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span></span></span><span class="" style="top: -0.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 3.5em;"><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: 4em;"><span class="" style="top: -6.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.0379em;">δ</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -4.66em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.0379em;">δ</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -3.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal" style="margin-right: 0.0379em;">δ</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -1.66em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal" style="margin-right: 0.0379em;">δ</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -0.16em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 3.5em;"><span class=""></span></span></span></span></span></span></span></span></span></span></span></span></p> <p>（不等式 <span class="katex--inline"><span class="katex"><span class="katex-mathml"> y ≥ − ( 1 − δ ) M y\geq -(1-\delta) M </span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.8304em; vertical-align: -0.1944em;"></span><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</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="mord">−</span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</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="mord mathnormal" style="margin-right: 0.0379em;">δ</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span></span></span> 不需要，因为自动满足）<br> <font color="red"><strong>上面第 2 个不等式也可以更简单地写成：</strong><br> <span class="katex--display"><span class="katex-display"><span class="katex"><span class="katex-mathml"> x ≥ y x\geq y </span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.7719em; vertical-align: -0.136em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right: 0.2778em;"></span></span><span class="base"><span class="strut" style="height: 0.625em; vertical-align: -0.1944em;"></span><span class="mord mathnormal" style="margin-right: 0.0359em;">y</span></span></span></span></span></span></font></p> <p>另外，假如有下面的 0-1 判断条件：<br> <span class="katex--display"><span class="katex-display"><span class="katex"><span class="katex-mathml"> x = { a z = 1 b z = 0 x=<span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display"><span class="MathJax MathJax_FullWidth" id="MathJax-Element-2-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mi>a</mi><mspace width="1em" /></mtd><mtd><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-60" style="width: 100%; display: inline-block; min-width: 5.976em;"><span style="display: inline-block; position: relative; width: 100%; height: 0px; font-size: 102%;"><span style="position: absolute; clip: rect(2.382em, 1005.82em, 5.115em, -999.997em); top: -3.997em; left: 0em; width: 100%;"><span class="mrow" id="MathJax-Span-61"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(2.382em, 1005.82em, 5.115em, -999.997em); top: -3.997em; left: 50%; margin-left: -2.934em;"><span class="mrow" id="MathJax-Span-62"><span class="mo" id="MathJax-Span-63" style="vertical-align: 0em;"><span style="font-family: MathJax_Size3;">{</span></span><span class="mtable" id="MathJax-Span-64" style="padding-right: 0.154em; padding-left: 0.154em;"><span style="display: inline-block; position: relative; width: 4.812em; height: 0px;"><span style="position: absolute; clip: rect(2.837em, 1001.52em, 4.812em, -999.997em); top: -3.997em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.521em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.394em, 1001.52em, 4.154em, -999.997em); top: -4.554em; left: 0em;"><span class="mtd" id="MathJax-Span-65"><span class="mrow" id="MathJax-Span-66"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1001.52em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.757em;"><span class="mi" id="MathJax-Span-67" style="font-family: MathJax_Math-italic;">a</span><span class="mspace" id="MathJax-Span-68" style="height: 0em; vertical-align: 0em; width: 1.015em; display: inline-block; overflow: hidden;"></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.141em, 1000.41em, 4.154em, -999.997em); top: -3.339em; left: 0em;"><span class="mtd" id="MathJax-Span-74"><span class="mrow" id="MathJax-Span-75"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1000.41em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.2em;"><span class="mi" id="MathJax-Span-76" style="font-family: MathJax_Math-italic;">b</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; clip: rect(2.635em, 1002.23em, 4.812em, -999.997em); top: -3.997em; left: 2.534em;"><span style="display: inline-block; position: relative; width: 2.281em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.192em, 1002.18em, 4.154em, -999.997em); top: -4.554em; left: 0em;"><span class="mtd" id="MathJax-Span-69"><span class="mrow" id="MathJax-Span-70"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.192em, 1002.18em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -1.111em;"><span class="mi" id="MathJax-Span-71" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-72" style="font-family: MathJax_Main; padding-left: 0.256em;">=</span><span class="mn" id="MathJax-Span-73" style="font-family: MathJax_Main; padding-left: 0.256em;">1</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.192em, 1002.23em, 4.154em, -999.997em); top: -3.339em; left: 0em;"><span class="mtd" id="MathJax-Span-77"><span class="mrow" id="MathJax-Span-78"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.192em, 1002.23em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -1.111em;"><span class="mi" id="MathJax-Span-79" style="font-family: MathJax_Math-italic;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-80" style="font-family: MathJax_Main; padding-left: 0.256em;">=</span><span class="mn" id="MathJax-Span-81" style="font-family: MathJax_Main; padding-left: 0.256em;">0</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span><span class="mo" id="MathJax-Span-82"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -1.03em; border-left: 0px solid; width: 0px; height: 2.533em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mo>{</mo><mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"><mtr><mtd><mi>a</mi><mspace width="1em"></mspace></mtd><mtd><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>b</mi></mtd><mtd><mi>z</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-2">\begin{cases} a\quad &z=1\\ b & z=0 \end{cases}</script> </span><span class="katex-html"><span class="base"><span class="strut" style="height: 0.4306em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span></span><span class="base"><span class="strut" style="height: 3em; vertical-align: -1.25em;"></span><span class="minner"><span class="mopen delimcenter" style="top: 0em;"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.69em;"><span class="" style="top: -3.69em;"><span class="pstrut" style="height: 3.008em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="mspace" style="margin-right: 1em;"></span></span></span><span class="" style="top: -2.25em;"><span class="pstrut" style="height: 3.008em;"></span><span class="mord"><span class="mord mathnormal">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 1.19em;"><span class=""></span></span></span></span></span><span class="arraycolsep" style="width: 1em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height: 1.69em;"><span class="" style="top: -3.69em;"><span class="pstrut" style="height: 3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord">1</span></span></span><span class="" style="top: -2.25em;"><span class="pstrut" style="height: 3.008em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 1.19em;"><span class=""></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></span></p> <p>则可以转化为下面的线性表达式：</p> <p><span class="katex--display"><span class="katex-display"><span class="katex"><span class="katex-mathml"> x ≤ a + ( 1 − z ) M x ≥ a − ( 1 − z ) M x ≤ b + z M x ≥ b − z M <span class="MathJax_Preview" style="color: inherit; display: none;"></span><div class="MathJax_Display"><span class="MathJax MathJax_FullWidth" id="MathJax-Element-3-Frame" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>a</mi><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>b</mi><mo>+</mo><mi>z</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>b</mi><mo>−</mo><mi>z</mi><mi>M</mi></mtd></mtr></mtable></math>" role="presentation" style="position: relative;"><nobr aria-hidden="true"><span class="math" id="MathJax-Span-83" style="width: 100%; display: inline-block; min-width: 7.849em;"><span style="display: inline-block; position: relative; width: 100%; height: 0px; font-size: 102%;"><span style="position: absolute; clip: rect(3.141em, 1007.7em, 8.406em, -999.997em); top: -6.022em; left: 0em; width: 100%;"><span class="mrow" id="MathJax-Span-84"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1007.7em, 8.406em, -999.997em); top: -6.022em; left: 50%; margin-left: -3.845em;"><span class="mtable" id="MathJax-Span-85" style="padding-left: 0.154em;"><span style="display: inline-block; position: relative; width: 7.545em; height: 0px;"><span style="position: absolute; clip: rect(2.939em, 1000.51em, 7.697em, -999.997em); top: -5.465em; left: 0em;"><span style="display: inline-block; position: relative; width: 0.559em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -5.971em; left: 0em;"><span class="mtd" id="MathJax-Span-86"><span class="mrow" id="MathJax-Span-87"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-88" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -4.604em; left: 0em;"><span class="mtd" id="MathJax-Span-101"><span class="mrow" id="MathJax-Span-102"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-103" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.237em; left: 0em;"><span class="mtd" id="MathJax-Span-116"><span class="mrow" id="MathJax-Span-117"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-118" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -1.972em; left: 0em;"><span class="mtd" id="MathJax-Span-127"><span class="mrow" id="MathJax-Span-128"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.394em, 1000.51em, 4.154em, -999.997em); top: -3.997em; left: 50%; margin-left: -0.301em;"><span class="mi" id="MathJax-Span-129" style="font-family: MathJax_Math-italic;">x</span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.47em;"></span></span><span style="position: absolute; clip: rect(3.04em, 1006.99em, 8.203em, -999.997em); top: -5.87em; left: 0.559em;"><span style="display: inline-block; position: relative; width: 6.988em; height: 0px;"><span style="position: absolute; width: 100%; clip: rect(3.091em, 1006.99em, 4.407em, -999.997em); top: -5.971em; left: 0em;"><span class="mtd" id="MathJax-Span-89"><span class="mrow" id="MathJax-Span-90"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.091em, 1006.99em, 4.407em, -999.997em); top: -3.997em; left: 50%; margin-left: -3.49em;"><span class="mi" id="MathJax-Span-91"></span><span class="mo" id="MathJax-Span-92" style="font-family: MathJax_Main; padding-left: 0.256em;">≤</span><span class="mi" id="MathJax-Span-93" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">a</span><span class="mo" id="MathJax-Span-94" style="font-family: MathJax_Main; padding-left: 0.205em;">+</span><span class="mo" id="MathJax-Span-95" style="font-family: MathJax_Main; padding-left: 0.205em;">(</span><span class="mn" id="MathJax-Span-96" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-97" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mi" id="MathJax-Span-98" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-99" style="font-family: MathJax_Main;">)</span><span class="mi" id="MathJax-Span-100" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.091em, 1006.99em, 4.407em, -999.997em); top: -4.604em; left: 0em;"><span class="mtd" id="MathJax-Span-104"><span class="mrow" id="MathJax-Span-105"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.091em, 1006.99em, 4.407em, -999.997em); top: -3.997em; left: 50%; margin-left: -3.49em;"><span class="mi" id="MathJax-Span-106"></span><span class="mo" id="MathJax-Span-107" style="font-family: MathJax_Main; padding-left: 0.256em;">≥</span><span class="mi" id="MathJax-Span-108" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">a</span><span class="mo" id="MathJax-Span-109" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mo" id="MathJax-Span-110" style="font-family: MathJax_Main; padding-left: 0.205em;">(</span><span class="mn" id="MathJax-Span-111" style="font-family: MathJax_Main;">1</span><span class="mo" id="MathJax-Span-112" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mi" id="MathJax-Span-113" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mo" id="MathJax-Span-114" style="font-family: MathJax_Main;">)</span><span class="mi" id="MathJax-Span-115" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.141em, 1004.41em, 4.305em, -999.997em); top: -3.237em; left: 0em;"><span class="mtd" id="MathJax-Span-119"><span class="mrow" id="MathJax-Span-120"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1004.41em, 4.305em, -999.997em); top: -3.997em; left: 50%; margin-left: -2.225em;"><span class="mi" id="MathJax-Span-121"></span><span class="mo" id="MathJax-Span-122" style="font-family: MathJax_Main; padding-left: 0.256em;">≤</span><span class="mi" id="MathJax-Span-123" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">b</span><span class="mo" id="MathJax-Span-124" style="font-family: MathJax_Main; padding-left: 0.205em;">+</span><span class="mi" id="MathJax-Span-125" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-126" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span><span style="position: absolute; width: 100%; clip: rect(3.141em, 1004.41em, 4.305em, -999.997em); top: -1.972em; left: 0em;"><span class="mtd" id="MathJax-Span-130"><span class="mrow" id="MathJax-Span-131"><span style="display: inline-block; position: relative; width: 100%; height: 0px;"><span style="position: absolute; clip: rect(3.141em, 1004.41em, 4.305em, -999.997em); top: -3.997em; left: 50%; margin-left: -2.225em;"><span class="mi" id="MathJax-Span-132"></span><span class="mo" id="MathJax-Span-133" style="font-family: MathJax_Main; padding-left: 0.256em;">≥</span><span class="mi" id="MathJax-Span-134" style="font-family: MathJax_Math-italic; padding-left: 0.256em;">b</span><span class="mo" id="MathJax-Span-135" style="font-family: MathJax_Main; padding-left: 0.205em;">−</span><span class="mi" id="MathJax-Span-136" style="font-family: MathJax_Math-italic; padding-left: 0.205em;">z<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span class="mi" id="MathJax-Span-137" style="font-family: MathJax_Math-italic;">M<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.104em;"></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 4.002em;"></span></span></span><span style="display: inline-block; width: 0px; height: 5.875em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.027em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 6.027em;"></span></span></span><span style="display: inline-block; overflow: hidden; vertical-align: -2.321em; border-left: 0px solid; width: 0px; height: 5.218em;"></span></span></nobr><span class="MJX_Assistive_MathML MJX_Assistive_MathML_Block" role="presentation"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>a</mi><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>a</mi><mo>−</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mo stretchy="false">)</mo><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≤</mo><mi>b</mi><mo>+</mo><mi>z</mi><mi>M</mi></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi></mi><mo>≥</mo><mi>b</mi><mo>−</mo><mi>z</mi><mi>M</mi></mtd></mtr></mtable></math></span></span></div><script type="math/tex; mode=display" id="MathJax-Element-3">\begin{aligned} x&\leq a+(1-z)M\\ x&\geq a-(1-z)M\\ x&\leq b+zM\\ x&\geq b-zM \end{aligned}</script> </span><span class="katex-html"><span class="base"><span class="strut" style="height: 6em; vertical-align: -2.75em;"></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: 3.25em;"><span class="" style="top: -5.41em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -3.91em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -2.41em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span><span class="" style="top: -0.91em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord mathnormal">x</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 2.75em;"><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: 3.25em;"><span class="" style="top: -5.41em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -3.91em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mclose">)</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -2.41em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span><span class="" style="top: -0.91em;"><span class="pstrut" style="height: 3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mrel">≥</span><span class="mspace" style="margin-right: 0.2778em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right: 0.2222em;"></span><span class="mord mathnormal" style="margin-right: 0.044em;">z</span><span class="mord mathnormal" style="margin-right: 0.109em;">M</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height: 2.75em;"><span class=""></span></span></span></span></span></span></span></span></span></span></span></span></p> <p>牢记这个小技巧非常方便！</p> </div> <link href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/editerView/markdown_views-f23dff6052.css" rel="stylesheet"> <link href="https://csdnimg.cn/release/blogv2/dist/mdeditor/css/style-c216769e99.css" rel="stylesheet"> <div><div><span>声明：</span>本文内容由网友自发贡献，不代表【wpsshop博客】立场，版权归原作者所有，本站不承担相应法律责任。如您发现有侵权的内容，请联系我们。转载请注明出处：<a href="https://www.wpsshop.cn/w/你好赵伟/article/detail/645114">https://www.wpsshop.cn/w/你好赵伟/article/detail/645114</a></div></div></div><div class="article_recommend"><div class="list_top">推荐阅读</div><div class="ListItems"><ul class="NewsList"><li><div class="NewTitle"><a title="article" class="cat" href="/article/list/1" target="_blank">article<i></i></a><a title="K8S认证|CKA题库+答案| 15. 备份还原Etcd" 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