Neural Network Toolbox™

1-D minimization using golden section search

Syntax

• [a,gX,perf,retcode,delta,tol] = 
  srchgol(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf)
  

Description

srchgol is a linear search routine. It searches in a given direction to locate the minimum of the performance function in that direction. It uses a technique called the golden section search.

srchgol(net,X,Pd,Tl,Ai,Q,TS,dX,gX,perf,dperf,delta,tol,ch_perf) takes these inputs,

net	Neural network
X	Vector containing current values of weights and biases
Pd	Delayed input vectors
Tl	Layer target vectors
Ai	Initial input delay conditions
Q	Batch size
TS	Time steps
dX	Search direction vector
gX	Gradient vector
perf	Performance value at current X
dperf	Slope of performance value at current X in direction of dX
delta	Initial step size
tol	Tolerance on search
ch_perf	Change in performance on previous step

and returns

a	Step size that minimizes performance
gX	Gradient at new minimum point
perf	Performance value at new minimum point
retcode	Return code that has three elements. The first two elements correspond to the number of function evaluations in the two stages of the search. The third element is a return code. These have different meanings for different search algorithms. Some might not be used in this function.
	0	Normal
	1	Minimum step taken
	2	Maximum step taken
	3	Beta condition not met
delta	New initial step size, based on the current step size
tol	New tolerance on search

Parameters used for the golden section algorithm are

alpha	Scale factor that determines sufficient reduction in perf
bmax	Largest step size
scale_tol	Parameter that relates the tolerance tol to the initial step size delta, usually set to 20

The defaults for these parameters are set in the training function that calls them. See traincgf, traincgb, traincgp, trainbfg, and trainoss.

Dimensions for these variables are

Pd	No x Ni x TS cell array	Each element P{i,j,ts} is a Dij x Q matrix.
Tl	Nl x TS cell array	Each element P{i,ts} is a Vi x Q matrix.
Ai	Nl x LD cell array	Each element Ai{i,k} is an Si x Q matrix.

where

Ni	=		net.numInputs
Nl	=		net.numLayers
LD	=		net.numLayerDelays
Ri	=		net.inputs{i}.size
Si	=		net.layers{i}.size
Vi	=		net.targets{i}.size
Dij	=		Ri * length(net.inputWeights{i,j}.delays)

Examples

Here is a problem consisting of inputs p and targets t to be solved with a network.

• p = [0 1 2 3 4 5];
  t = [0 0 0 1 1 1];
  

A two-layer feed-forward network is created. The network's input ranges from [0 to 10]. The first layer has two tansig neurons, and the second layer has one logsig neuron. The traincgf network training function and the srchgol search function are to be used.

Create and Test a Network

• net = newff([0 5],[2 1],{'tansig','logsig'},'traincgf');
  a = sim(net,p)
  
  Train and Retest the Network
  net.trainParam.searchFcn = 'srchgol';
  net.trainParam.epochs = 50;
  net.trainParam.show = 10;
  net.trainParam.goal = 0.1;
  net = train(net,p,t);
  a = sim(net,p)
  

Network Use

You can create a standard network that uses srchgol with newff, newcf, or newelm.

To prepare a custom network to be trained with traincgf, using the line search function srchgol,

1. Set net.trainFcn to 'traincgf'. This sets net.trainParam to traincgf's default parameters.
2. Set net.trainParam.searchFcn to 'srchgol'.

The srchgol function can be used with any of the following training functions: traincgf, traincgb, traincgp, trainbfg, trainoss.

Algorithm

srchgol locates the minimum of the performance function in the search direction dX, using the golden section search. It is based on the algorithm as described on page 33 of Scales (see reference below).

Reference

Scales, L.E., Introduction to Non-Linear Optimization, New York, Springer-Verlag, 1985

See Also

srchbac, srchbre, srchcha, srchhyb

Provide feedback about this page

srchcha

srchhyb

© 1984-2008- The MathWorks, Inc.    -   Site Help   -   Patents   -   Trademarks   -   Privacy Policy   -   Preventing Piracy   -   RSS