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<title>GNU Scientific Library &ndash; Reference Manual: Multimin Stopping Criteria</title>

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<a name="Multimin-Stopping-Criteria"></a>
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<p>
Next: <a href="Multimin-Algorithms-with-Derivatives.html#Multimin-Algorithms-with-Derivatives" accesskey="n" rel="next">Multimin Algorithms with Derivatives</a>, Previous: <a href="Multimin-Iteration.html#Multimin-Iteration" accesskey="p" rel="previous">Multimin Iteration</a>, Up: <a href="Multidimensional-Minimization.html#Multidimensional-Minimization" accesskey="u" rel="up">Multidimensional Minimization</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Stopping-Criteria"></a>
<h3 class="section">37.6 Stopping Criteria</h3>

<p>A minimization procedure should stop when one of the following
conditions is true:
</p>
<ul>
<li> A minimum has been found to within the user-specified precision.

</li><li> A user-specified maximum number of iterations has been reached.

</li><li> An error has occurred.
</li></ul>

<p>The handling of these conditions is under user control.  The functions
below allow the user to test the precision of the current result.
</p>
<dl>
<dt><a name="index-gsl_005fmultimin_005ftest_005fgradient"></a>Function: <em>int</em> <strong>gsl_multimin_test_gradient</strong> <em>(const gsl_vector * <var>g</var>, double <var>epsabs</var>)</em></dt>
<dd><p>This function tests the norm of the gradient <var>g</var> against the
absolute tolerance <var>epsabs</var>. The gradient of a multidimensional
function goes to zero at a minimum. The test returns <code>GSL_SUCCESS</code>
if the following condition is achieved,
</p>
<div class="example">
<pre class="example">|g| &lt; epsabs
</pre></div>

<p>and returns <code>GSL_CONTINUE</code> otherwise.  A suitable choice of
<var>epsabs</var> can be made from the desired accuracy in the function for
small variations in <em>x</em>.  The relationship between these quantities
is given by <em>\delta f = g \delta x</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fmultimin_005ftest_005fsize"></a>Function: <em>int</em> <strong>gsl_multimin_test_size</strong> <em>(const double <var>size</var>, double <var>epsabs</var>)</em></dt>
<dd><p>This function tests the minimizer specific characteristic
size (if applicable to the used minimizer) against absolute tolerance <var>epsabs</var>. 
The test returns <code>GSL_SUCCESS</code> if the size is smaller than tolerance,
otherwise <code>GSL_CONTINUE</code> is returned.
</p></dd></dl>




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