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des_automata.html

@@ -2143,16 +2143,16 @@ <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) = [0, 1, 1, 2]
-output(dtr) = [0, 1, 0, 1]
-(update!(dtr), output(dtr)) = ([0, 0, 1, 1], [0, 0, 1, 0])
-(update!(dtr), output(dtr)) = ([0, 0, 0, 1], [0, 0, 0, 1])
-(update!(dtr), output(dtr)) = ([0, 0, 0, 0], [1, 0, 0, 0])
-(update!(dtr), output(dtr)) = ([1, 0, 0, 0], [0, 1, 0, 0])
-(update!(dtr), output(dtr)) = ([1, 1, 0, 0], [0, 0, 1, 0])</code></pre>
+<pre><code>x_initial = rand(0:k, n) = [0, 4, 0, 4]
+output(dtr) = [0, 1, 1, 1]
+(update!(dtr), output(dtr)) = ([0, 0, 4, 0], [1, 0, 1, 1])
+(update!(dtr), output(dtr)) = ([1, 0, 0, 4], [0, 1, 0, 1])
+(update!(dtr), output(dtr)) = ([1, 1, 0, 0], [0, 0, 1, 0])
+(update!(dtr), output(dtr)) = ([1, 1, 1, 0], [0, 0, 0, 1])
+(update!(dtr), output(dtr)) = ([1, 1, 1, 1], [1, 0, 0, 0])</code></pre>
 </div>
 <div class="cell-output cell-output-display" data-execution_count="1">
-<pre><code>([1, 1, 0, 0], [0, 0, 1, 0])</code></pre>
+<pre><code>([1, 1, 1, 1], [1, 0, 0, 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>

mld_software.html

@@ -715,7 +715,7 @@ <h2 class="anchored" data-anchor-id="support-for-indicator-constraints-in-optimi
 f(\bm x) &amp;\leq (1-\delta) M,\\
 f(\bm x) &amp;\geq \epsilon + (m-\epsilon)\delta
 \end{aligned}
-</span> using a sufficiently large constant <span class="math inline">M</span> and a sufficiently small constant <span class="math inline">m</span>. But some solvers for mixed integer programming/optimization support the indicator constraints directly, without the need to come up with <span class="math inline">M</span> and <span class="math inline">m</span>. As a matter of fact, only one of the two implications, namely <span class="math display">
+</span> using a sufficiently large constant <span class="math inline">M</span> and a sufficiently small constant <span class="math inline">m</span>. But some solvers for mixed integer programming/optimization support the indicator constraints directly, without the need to come up with <span class="math inline">M</span> and <span class="math inline">m</span>. As a matter of fact, the support is only provided for one of the two implications, namely <span class="math display">
 [\delta = 1] \rightarrow [f(\bm x) \leq 0].
 </span></p>
 <p>Gurobi does provide such <a href="https://docs.gurobi.com/projects/optimizer/en/current/concepts/modeling/constraints.html#simple-constraints">support for indicator constraints</a>, the increasingly popular free&amp;open-source <a href="https://highs.dev">HiGHS</a> does not, …</p>
@@ -737,9 +737,10 @@ <h2 class="anchored" data-anchor-id="support-for-indicator-constraints-in-optimi
 </div>
 <p>With Python API of Gurobi, the indicator constraints can be added using <a href="https://docs.gurobi.com/projects/optimizer/en/current/reference/python/model.html#Model.addGenConstrIndicator">addGenContstrIndicator</a> function. One possible syntax is</p>
 <pre><code>model.addConstr((delta == 1) &gt;&gt; (x + y - 1.0 &lt;= 0.0))</code></pre>
-<p>The other direction of implication is not supported by optimization solvers (at least not that we know of). Therefore it has no support in optimization modellers such as JuMP either. In order to handle it, besides resorting to the Big-M method, we can also use the equivalent formulation <span class="math display">
+<p>The other direction of implication is not supported by optimization solvers. Therefore it has no support in optimization modellers such as JuMP either. In order to handle it, besides resorting to the Big-M method, we can also use the equivalent formulation <span class="math display">
 [\delta = 0] \rightarrow [f(\bm x) \geq \epsilon],
 </span> where some small <span class="math inline">\epsilon \geq 0</span> had to be added to turn the strict inequality into a non-strict one.</p>
+<p>Note, however, that it is not universally recommendable to rely on the support of the mixed integer solver for the indicator constraints. The reason is that sometimes the solvers may decide to reformulate the indicator constraints using the Big-M method by themselves, in which case we have no direct control over the choice of <span class="math inline">M</span>.</p>
 
 
 </section>