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hurak · Dec 10, 2024 · 08252a1 · 08252a1
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diff --git a/.nojekyll b/.nojekyll
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diff --git a/classes_reset 14.html b/classes_reset 14.html
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diff --git a/complementarity_references 23.html b/complementarity_references 23.html
diff --git a/complementarity_simulations 13.html b/complementarity_simulations 13.html
diff --git a/complementarity_simulations.html b/complementarity_simulations.html
diff --git a/complementarity_simulations_files/figure-html/fig-state-portrait-output-2.svg b/complementarity_simulations_files/figure-html/fig-state-portrait-output-2.svg
diff --git a/complementarity_software.html b/complementarity_software.html
@@ -662,7 +662,7 @@ <h2 class="anchored" data-anchor-id="solving-optimization-problems-with-compleme
 </ul>
 <p>When restricted to Matlab, there are several options, all of them commercial:</p>
 <ul>
-<li><a href="https://www.mathworks.com/help/optim/index.html">Optimization Toolbox for Matlab</a> does not offer a specialized solver for complementarity problems. The <code>fmincon</code> function can only handle it as a general nonlinear constraint <span class="math inline">g_1(x)g_2(x)</span>.</li>
+<li><a href="https://www.mathworks.com/help/optim/index.html">Optimization Toolbox for Matlab</a> does not offer a specialized solver for complementarity problems. The <code>fmincon</code> function can only handle it as a general nonlinear constraint <span class="math inline">g_1(x)g_2(x)=0, \, g_1(x) \geq 0, \, g_2(x) \geq 0</span>.</li>
 <li><a href="https://tomopt.com/tomlab/">Tomlab</a> toolbox has some <a href="https://tomopt.com/docs/quickguide/quickguide029.php">support for complementarity constraints</a>.</li>
 <li><a href="https://www.artelys.com/solvers/knitro/">Knitro</a> solver (by Artelys) has some <a href="https://www.artelys.com/docs/knitro/2_userGuide/complementarity.html">support for complementarity constraints</a>.</li>
 <li><a href="https://yalmip.github.io">YALMIP</a> toolbox supports definining the complementarity constraints through the command <a href="https://yalmip.github.io/command/complements/">complements</a>: <code>F = complements(w &gt;= 0, z &gt;= 0)</code>. By default, it converts the problem into the format suitable for a mixed-integer solver. If Knitro is available, it can be interfaced.</li>

diff --git a/des_automata 22.html b/des_automata 22.html
diff --git a/des_automata.html b/des_automata.html
@@ -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) = [1, 0, 4, 3]
+<pre><code>x_initial = rand(0:k, n) = [4, 0, 3, 2]
 output(dtr) = [0, 1, 1, 1]
-(update!(dtr), output(dtr)) = ([1, 1, 0, 4], [0, 0, 1, 1])
-(update!(dtr), output(dtr)) = ([1, 1, 1, 0], [0, 0, 0, 1])
-(update!(dtr), output(dtr)) = ([1, 1, 1, 1], [1, 0, 0, 0])
-(update!(dtr), output(dtr)) = ([2, 1, 1, 1], [0, 1, 0, 0])
-(update!(dtr), output(dtr)) = ([2, 2, 1, 1], [0, 0, 1, 0])</code></pre>
+(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>
 </div>
 <div class="cell-output cell-output-display" data-execution_count="1">
-<pre><code>([2, 2, 1, 1], [0, 0, 1, 0])</code></pre>
+<pre><code>([1, 1, 4, 4], [0, 0, 1, 0])</code></pre>
 </div>
 </div>
 <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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diff --git a/hybrid_equations 14.html b/hybrid_equations 14.html
diff --git a/hybrid_equations.html b/hybrid_equations.html
diff --git a/hybrid_equations_references 23.html b/hybrid_equations_references 23.html
diff --git a/intro_outline 24.html b/intro_outline 24.html
diff --git a/max_plus_algebra 12.html b/max_plus_algebra 12.html
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diff --git a/max_plus_systems 18.html b/max_plus_systems 18.html
diff --git a/mld_DHA 23.html b/mld_DHA 23.html
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diff --git a/mld_software 4.html b/mld_software 4.html
diff --git a/mpc_mld_references 23.html b/mpc_mld_references 23.html
diff --git a/mpc_mld_software 23.html b/mpc_mld_software 23.html
diff --git a/petri_nets 10.html b/petri_nets 10.html
diff --git a/petri_nets_references 23.html b/petri_nets_references 23.html
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diff --git a/search.json b/search.json
diff --git a/sitemap.xml b/sitemap.xml
@@ -90,7 +90,7 @@
   </url>
   <url>
     <loc>https://hurak.github.io/hys/complementarity_software.html</loc>
-    <lastmod>2024-09-09T19:06:06.203Z</lastmod>
+    <lastmod>2024-12-09T23:26:01.667Z</lastmod>
   </url>
   <url>
     <loc>https://hurak.github.io/hys/stability_via_common_lyapunov_function.html</loc>

diff --git a/stability_recap 23.html b/stability_recap 23.html
diff --git a/stability_via_multiple_lyapunov_function 24.html b/stability_via_multiple_lyapunov_function 24.html
diff --git a/stability_via_multiple_lyapunov_function.html b/stability_via_multiple_lyapunov_function.html
@@ -784,7 +784,7 @@ <h1 class="title">Stability via multiple Lyapunov functions</h1>
    │     └─ Convex.NegateAtom (affine; real)
    │        └─ …
    ├─ PSD constraint (convex)
-   │  └─ 2×2 real variable (id: 126…042)
+   │  └─ 2×2 real variable (id: 440…606)
    ⋮</code></pre>
 </div>
 </div>

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