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hurak committed Dec 14, 2024
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2 changes: 1 addition & 1 deletion .nojekyll
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4 changes: 2 additions & 2 deletions complementarity_constraints.html
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Expand Up @@ -705,8 +705,8 @@ <h2 class="anchored" data-anchor-id="geometric-interpretation-of-complementarity
</div>
<p>Optimization over these constraints is difficult, and not only because the feasible set is nonconvex, but also because <em>constraint qualification</em> conditions are not satisfied. Still, some results and tools are available for some classes of optimization problems with these constraints.</p>
</section>
<section id="linear-complementarity-problem-lcp" class="level2 scrollable">
<h2 class="scrollable anchored" data-anchor-id="linear-complementarity-problem-lcp">Linear complementarity problem (LCP)</h2>
<section id="linear-complementarity-problem-lcp" class="level2">
<h2 class="anchored" data-anchor-id="linear-complementarity-problem-lcp">Linear complementarity problem (LCP)</h2>
<p>For a given square matrix <span class="math inline">\mathbf M</span> and a vector <span class="math inline">\mathbf q</span> , the <em>linear complementarity problem</em> (LCP) asks for finding two vectors <span class="math inline">\bm w</span> and <span class="math inline">\bm z</span> satisfying <span class="math display">
\begin{aligned}
\bm w-\mathbf M\bm z &amp;= \mathbf q \\
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1,105 changes: 1,105 additions & 0 deletions complementarity_references 24.html

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1,506 changes: 957 additions & 549 deletions complementarity_simulations.html

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3,336 changes: 3,336 additions & 0 deletions des_automata 23.html

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14 changes: 7 additions & 7 deletions des_automata.html
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Expand Up @@ -2131,16 +2131,16 @@ <h3 class="anchored" data-anchor-id="mealy-machine">Mealy machine</h3>
<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a><span class="pp">@show</span> <span class="fu">update!</span>(dtr), <span class="fu">output</span>(dtr)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</details>
<div class="cell-output cell-output-stdout">
<pre><code>x_initial = rand(0:k, n) = [4, 0, 3, 2]
<pre><code>x_initial = rand(0:k, n) = [2, 0, 2, 3]
output(dtr) = [0, 1, 1, 1]
(update!(dtr), output(dtr)) = ([4, 4, 0, 3], [0, 0, 1, 1])
(update!(dtr), output(dtr)) = ([4, 4, 4, 0], [0, 0, 0, 1])
(update!(dtr), output(dtr)) = ([4, 4, 4, 4], [1, 0, 0, 0])
(update!(dtr), output(dtr)) = ([1, 4, 4, 4], [0, 1, 0, 0])
(update!(dtr), output(dtr)) = ([1, 1, 4, 4], [0, 0, 1, 0])</code></pre>
(update!(dtr), output(dtr)) = ([2, 2, 0, 2], [1, 0, 1, 1])
(update!(dtr), output(dtr)) = ([3, 2, 2, 0], [0, 1, 0, 1])
(update!(dtr), output(dtr)) = ([3, 3, 2, 2], [0, 0, 1, 0])
(update!(dtr), output(dtr)) = ([3, 3, 3, 2], [0, 0, 0, 1])
(update!(dtr), output(dtr)) = ([3, 3, 3, 3], [1, 0, 0, 0])</code></pre>
</div>
<div class="cell-output cell-output-display" data-execution_count="1">
<pre><code>([1, 1, 4, 4], [0, 0, 1, 0])</code></pre>
<pre><code>([3, 3, 3, 3], [1, 0, 0, 0])</code></pre>
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<p>We can see that although initially the there can be more tokens, after a few iterations the algorithm achieves the goal of having just one token in the ring.</p>
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