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<A NAME=num_min>

<TITLE>num_min</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>NUM_MIN</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
 <P>
<P>
The Fletcher Reeves version of the <em>steepest descent</em> 
algorithms is used to find the <em>minimum</em> of a 
function of one or more variables. The 
function must have continuous partial derivatives with respect to all 
variables. The starting point of the search can be 
specified; if not, random values are taken instead. 
The steepest descent algorithms in general find only local 
minima. 
 <P>
<P>
 <P> <H3> 
syntax: </H3>
<em>num_min</em>(&lt;exp&gt;, 
 &lt;var&gt;[=&lt;val&gt;] [,&lt;var&gt;[=&lt;val&gt;] ... 
 [,accuracy=&lt;a&gt;] [,iterations=&lt;i&gt;]) 
<P>
<P>
or 
<P>
<P>
<em>num_min</em>(exp, { 
 &lt;var&gt;[=&lt;val&gt;] [,&lt;var&gt;[=&lt;val&gt;] ...] } 
 [,accuracy=&lt;a&gt;] [,iterations=&lt;i&gt;]) 
<P>
<P>
<P>
where &lt;exp&gt; is a function expression, 
&lt;var&gt; are the variables in &lt;exp&gt; and 
&lt;val&gt; are the (optional) start values. 
For &lt;a&gt; and &lt;i&gt; see 
<A HREF=r37_0423.html>numeric accuracy</A>. 
<P>
<P>
<em>Num_min</em>tries to find the next local minimum along the descending 
path starting at the given point. The result is a 
<A HREF=r37_0053.html>list</A> 
with the minimum function value as first element followed by a list 
of 
<A HREF=r37_0045.html>equation</A><em>s</em>, where the variables are equated to
 the coordinates 
of the result point. 
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
num_min(sin(x)+x/5, x)

  {4.9489585606,{X=29.643767785}}


num_min(sin(x)+x/5, x=0)

  { - 1.3342267466,{X= - 1.7721582671}}

</TT></PRE><P>