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<html><head><title>Netlab Reference Manual quasinew</title></head><body><H1> quasinew</H1><h2>Purpose</h2>Quasi-Newton optimization.<p><h2>Description</h2><CODE>[x, options, flog, pointlog] = quasinew(f, x, options, gradf)</CODE> uses a quasi-Newtonalgorithm to find a local minimum of the function <CODE>f(x)</CODE> whosegradient is given by <CODE>gradf(x)</CODE>. Here <CODE>x</CODE> is a row vectorand <CODE>f</CODE> returns a scalar value. The point at which <CODE>f</CODE> has a local minimumis returned as <CODE>x</CODE>. The function value at that point is returnedin <CODE>options(8)</CODE>. A log of the function valuesafter each cycle is (optionally) returned in <CODE>flog</CODE>, and a logof the points visited is (optionally) returned in <CODE>pointlog</CODE>.<p><CODE>quasinew(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 visitedin 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 valueof <CODE>x</CODE> at the solution. If the absolute difference betweenthe 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 objectivefunction at the solution. If the absolute difference between theobjective 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 besatisfied for termination.<p><CODE>options(9)</CODE> should be set to 1 to check the user defined gradientfunction.<p><CODE>options(10)</CODE> returns the total number of function evaluations (includingthose 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-2</CODE>.<p><h2>Examples</h2>An example of the use of the additional arguments is the minimization of an errorfunction for a neural network:<PRE>w = quasinew('neterr', w, options, 'netgrad', net, x, t);</PRE><p><h2>Algorithm</h2>The quasi-Newton algorithm builds up anapproximation to the inverse Hessian over a number of steps. Themethod requires order W squared storage, where W is the number of functionparameters. The Broyden-Fletcher-Goldfarb-Shanno formula for theinverse Hessian updates is used. The line searches are carried out toa relatively low precision (1.0e-2).<p><h2>See Also</h2><CODE><a href="conjgrad.htm">conjgrad</a></CODE>, <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="scg.htm">scg</a></CODE><hr><b>Pages:</b><a href="index.htm">Index</a><hr><p>Copyright (c) Ian T Nabney (1996-9)</body></html>?? 快捷鍵說明
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