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<a name="Examples-for-cobyla"></a>
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<p>
Previous: <a href="maxima_200.html#Functions-and-Variables-for-cobyla" accesskey="p" rel="previous">Functions and Variables for cobyla</a>, Up: <a href="maxima_198.html#cobyla_002dpkg" accesskey="u" rel="up">cobyla-pkg</a> [<a href="maxima_toc.html#SEC_Contents" title="Table of contents" rel="contents">Contents</a>][<a href="maxima_423.html#Function-and-Variable-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Examples-for-cobyla-1"></a>
<h3 class="section">47.3 Examples for cobyla</h3>
<p>Minimize
\(x_1 x_2\) with
\(1-x_1^2-x_2^2 \ge 0.\)</p>
<p>The theoretical solution is
$$
\eqalign{
x_1 &= {1\over \sqrt{2}} \cr
x_2 &= -{1\over \sqrt{2}}
}
$$</p>
<div class="example">
<pre class="example">(%i1) load("fmin_cobyla")$
</pre><pre class="example">(%i2) fmin_cobyla(x1*x2, [x1, x2], [1,1],
constraints = [x1^2+x2^2<=1], iprint=1);
</pre><pre class="example"> Normal return from subroutine COBYLA
NFVALS = 66 F =-5.000000E-01 MAXCV = 1.999845E-12
X = 7.071058E-01 -7.071077E-01
(%o2) [[x1 = 0.70710584934848, x2 = - 0.7071077130248],
- 0.49999999999926, [[-1.999955756559757e-12],[]], 66]
</pre></div>
<p>Here is the same example but the constraint
is
\(x_1^2+x_2^2 \le -1\) which
is impossible over the reals.
</p>
<div class="example">
<pre class="example">(%i1) fmin_cobyla(x1*x2, [x1, x2], [1,1],
constraints = [x1^2+x2^2 <= -1], iprint=1);
</pre><pre class="example"> Normal return from subroutine COBYLA
NFVALS = 65 F = 3.016417E-13 MAXCV = 1.000000E+00
X =-3.375179E-07 -8.937057E-07
(%o1) [[x1 = - 3.375178983064622e-7, x2 = - 8.937056510780022e-7],
3.016416530564557e-13, 65, - 1]
(%i2) subst(%o1[2], [x1^2+x2^2 <= -1]);
(%o2) [- 6.847914590915444e-13 <= - 1]
</pre></div>
<p>We see the return code (<code>%o1[4]</code>) is -1 indicating that the
constraints may not be satisfied. Substituting the solution into the
constraint equation as shown in <code>%o2</code> shows that the constraint
is, of course, violated.
</p>
<p>There are additional examples in the share/cobyla/ex directory and in
share/cobyla/rtest_cobyla.mac.
</p>
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