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Netlab Reference Manual conjgrad
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<H1> conjgrad
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<h2>
Purpose
</h2>
Conjugate gradients optimization.

<p><h2>
Description
</h2>
<CODE>[x, options, flog, pointlog] = conjgrad(f, x, options, gradf)</CODE> uses a
conjugate gradients
algorithm to find the minimum of the function <CODE>f(x)</CODE> whose
gradient is given by <CODE>gradf(x)</CODE>.  Here <CODE>x</CODE> is a row vector
and <CODE>f</CODE> returns a scalar value.
The point at which <CODE>f</CODE> has a local minimum
is returned as <CODE>x</CODE>.  The function value at that point is returned
in <CODE>options(8)</CODE>.  A log of the function values
after each cycle is (optionally) returned in <CODE>flog</CODE>, and a log
of the points visited is (optionally) returned in <CODE>pointlog</CODE>.

<p><CODE>conjgrad(f, x, options, gradf, p1, p2, ...)</CODE> allows
additional arguments to be passed to <CODE>f()</CODE> and <CODE>gradf()</CODE>.

<p>The optional parameters have the following interpretations.

<p><CODE>options(1)</CODE> is set to 1 to display error values; also logs error
values in the return argument <CODE>errlog</CODE>, and the points visited
in the return argument <CODE>pointslog</CODE>.  If <CODE>options(1)</CODE> is set to 0,
then only warning messages are displayed.  If <CODE>options(1)</CODE> is -1,
then nothing is displayed.

<p><CODE>options(2)</CODE> is a measure of the absolute precision required for the value
of <CODE>x</CODE> at the solution.  If the absolute difference between
the values of <CODE>x</CODE> between two successive steps is less than
<CODE>options(2)</CODE>, then this condition is satisfied.

<p><CODE>options(3)</CODE> is a measure of the precision required of the objective
function at the solution.  If the absolute difference between the
objective function values between two successive steps is less than
<CODE>options(3)</CODE>, then this condition is satisfied.
Both this and the previous condition must be
satisfied for termination.

<p><CODE>options(9)</CODE> is set to 1 to check the user defined gradient function.

<p><CODE>options(10)</CODE> returns the total number of function evaluations (including
those in any line searches).

<p><CODE>options(11)</CODE> returns the total number of gradient evaluations.

<p><CODE>options(14)</CODE> is the maximum number of iterations; default 100.

<p><CODE>options(15)</CODE> is the precision in parameter space of the line search;
default <CODE>1e-4</CODE>.

<p><h2>
Examples
</h2>
An example of
the use of the additional arguments is the minimization of an error
function for a neural network:
<PRE>

w = quasinew('neterr', w, options, 'netgrad', net, x, t);
</PRE>


<p><h2>
Algorithm
</h2>

The conjugate gradients algorithm constructs search
directions <CODE>di</CODE> that are conjugate: i.e. <CODE>di*H*d(i-1) = 0</CODE>,
where <CODE>H</CODE> is the Hessian matrix.  This means that minimising along
<CODE>di</CODE> does not undo the effect of minimising along the previous
direction. The Polak-Ribiere formula is used to calculate new search
directions. The Hessian is not calculated, so there is only an
<CODE>O(W)</CODE> storage requirement (where <CODE>W</CODE> is the number of
parameters).  However, relatively accurate line searches must be used
(default is <CODE>1e-04</CODE>).

<p><h2>
See Also
</h2>
<CODE><a href="graddesc.htm">graddesc</a></CODE>, <CODE><a href="linemin.htm">linemin</a></CODE>, <CODE><a href="minbrack.htm">minbrack</a></CODE>, <CODE><a href="quasinew.htm">quasinew</a></CODE>, <CODE><a href="scg.htm">scg</a></CODE><hr>
<b>Pages:</b>
<a href="index.htm">Index</a>
<hr>
<p>Copyright (c) Ian T Nabney (1996-9)


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author	wolffd
date	Tue, 10 Feb 2015 15:05:51 +0000
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