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@@ -636,7 +638,7 @@ <h1 class="title">JuMP Syntax Cheatsheet</h1>
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<section id="basic-setup" class="level1">
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<h1>Basic Setup</h1>
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<div id="63c236e4" class="cell" data-execution_count="2">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">JuMP</span>, <span class="bu">HiGHS</span></span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co"># Create a model</span></span>
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<h1>Variables</h1>
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<section id="declaration" class="level2">
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<h2 class="anchored" data-anchor-id="declaration">Declaration</h2>
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<div id="538f1bda" class="cell" data-execution_count="3">
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<div id="dc9cbab1" class="cell" data-execution_count="3">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Continuous Variables</span></span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, x) <span class="co"># Unbounded continuous</span></span>
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<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, x <span class="op">&gt;=</span> <span class="fl">0</span>) <span class="co"># Non-negative continuous</span></span>
@@ -667,7 +669,7 @@ <h2 class="anchored" data-anchor-id="declaration">Declaration</h2>
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</section>
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<section id="containers" class="level2">
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<h2 class="anchored" data-anchor-id="containers">Containers</h2>
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<div id="2d937926" class="cell" data-execution_count="4">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Arrays</span></span>
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<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, x[<span class="fl">1</span><span class="op">:</span><span class="fl">5</span>]) <span class="co"># Array of 5 variables</span></span>
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<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, x[<span class="fl">1</span><span class="op">:</span><span class="fl">5</span>] <span class="op">&gt;=</span> <span class="fl">0</span>) <span class="co"># Non-negative array</span></span>
@@ -688,15 +690,15 @@ <h2 class="anchored" data-anchor-id="containers">Containers</h2>
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<h1>Constraints</h1>
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<section id="declaration-1" class="level2">
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<h2 class="anchored" data-anchor-id="declaration-1">Declaration</h2>
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<div id="c677a665" class="cell" data-execution_count="5">
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<div id="13a0115e" class="cell" data-execution_count="5">
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Basic constraints</span></span>
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<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@constraint</span>(model, con1, <span class="fl">2</span>x <span class="op">+</span> y <span class="op">&lt;=</span> <span class="fl">10</span>)</span>
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<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a><span class="pp">@constraint</span>(model, con2, x <span class="op">+</span> <span class="fl">2</span>y <span class="op">&gt;=</span> <span class="fl">5</span>)</span></code></pre></div><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></div>
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</div>
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</section>
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<section id="containers-1" class="level2">
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<h2 class="anchored" data-anchor-id="containers-1">Containers</h2>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb5"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Array of variables</span></span>
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<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, x[<span class="fl">1</span><span class="op">:</span><span class="fl">5</span>] <span class="op">&gt;=</span> <span class="fl">0</span>)</span>
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</section>
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<section id="conditional" class="level2">
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<h2 class="anchored" data-anchor-id="conditional">Conditional</h2>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Basic conditional constraint</span></span>
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<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@constraint</span>(model, cond[i<span class="op">=</span><span class="fl">1</span><span class="op">:</span><span class="fl">5</span>; i <span class="op">&gt;</span> <span class="fl">2</span>],</span>
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<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> x[i] <span class="op">&lt;=</span> <span class="fl">10</span></span>
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</section>
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<section id="conditions-while-summing" class="level2">
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<h2 class="anchored" data-anchor-id="conditions-while-summing">Conditions while Summing</h2>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb7"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="pp">@constraint</span>(model, total_sum,</span>
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<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">sum</span>(x[i] <span class="cf">for</span> i <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="fl">5</span> <span class="cf">if</span> i <span class="op">&gt;</span> <span class="fl">2</span>) <span class="op">&lt;=</span> <span class="fl">500</span></span>
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<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>)</span>
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<h2 class="anchored" data-anchor-id="declaration-2">Declaration</h2>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb8"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Maximize objective</span></span>
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<div class="code-copy-outer-scaffold"><div class="sourceCode cell-code" id="cb9"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co"># Container objective</span></span>
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<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a><span class="pp">@variable</span>(model, z[<span class="fl">1</span><span class="op">:</span><span class="fl">10</span>])</span>
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<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="pp">@objective</span>(model, Min, <span class="fu">sum</span>(z[i] <span class="cf">for</span> i <span class="kw">in</span> <span class="fl">1</span><span class="op">:</span><span class="fl">10</span>))</span>
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<h1>Additional Features</h1>
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<section id="checking-bounds" class="level2">
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<h2 class="anchored" data-anchor-id="checking-bounds">Checking Bounds</h2>
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<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="fu">has_lower_bound</span>(x) <span class="co"># Check if lower bound exists</span></span>
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<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="fu">has_upper_bound</span>(x) <span class="co"># Check if upper bound exists</span></span>
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<h2 class="anchored" data-anchor-id="checking-properties">Checking Properties</h2>
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<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>model <span class="op">=</span> <span class="fu">Model</span>(HiGHS.Optimizer)</span>
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<h2 class="anchored" data-anchor-id="solution-status-checks">Solution Status Checks</h2>
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<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>status <span class="op">=</span> <span class="fu">termination_status</span>(model) <span class="co"># Get solution status</span></span>
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<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>is_optimal <span class="op">=</span> status <span class="op">==</span> MOI.OPTIMAL <span class="co"># Check if optimal</span></span>

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