com.numericalmethod.suanshu.optimization.unconstrained.linesearch
Class Fletcher

java.lang.Object
  com.numericalmethod.suanshu.optimization.unconstrained.linesearch.Fletcher

public class Fletcher
extends java.lang.Object

This is the Fletcher's inexact line search method.

An inexact search is usually used in conjunction with a multi-dimensional optimization algorithm. It trades off the accuracy of the search result with the amount of computation. A lot of optimization algorithms are shown to be quite tolerant to line search imprecision.

See Also:

• "Algorithms 4.6, 7.3. Practical Optimization: Algorithms and Engineering Applications. Andreas Antoniou, Wu-Sheng Lu."
• "Section 2.6. Practical Methods of Optimization, Volume 1: Unconstrained Optimization. R. Fletcher."

Field Summary

double	chi parameter chi ensures that the result is not too close to the boundary
int	maxIterations the maximum number of iterations
double	rho the precision parameter rho The smaller it is, e.g., 0.1, the more accurate the result is.
double	sigma the precision parameter sigma The smaller it is, e.g., 0.1, the more accurate the result is.
double	tau parameter tau ensures that the result is not too close to the boundary
double	tol the convergence tolerance

Constructor Summary

Fletcher(double rho, double sigma, double tau, double chi, RealScalarFunction f, RealVectorFunction gradient, double tol, int maxIterations)
Construct a Fletcher instance to minimize a function f.

Fletcher(RealScalarFunction f, RealVectorFunction gradient)
Construct a Fletcher instance to minimize a function f with the default control parameters.

Method Summary

double

search(Vector x, Vector d) Get a so that f(x + a * d) is (approximately) minimized.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

rho

public final double rho

the precision parameter rho

The smaller it is, e.g., 0.1, the more accurate the result is.

sigma

public final double sigma

the precision parameter sigma

The smaller it is, e.g., 0.1, the more accurate the result is.

tau

public final double tau

parameter tau ensures that the result is not too close to the boundary

chi

public final double chi

parameter chi ensures that the result is not too close to the boundary

tol

public final double tol

the convergence tolerance

maxIterations

public final int maxIterations

the maximum number of iterations

Constructor Detail

Fletcher

public Fletcher(double rho,
                double sigma,
                double tau,
                double chi,
                RealScalarFunction f,
                RealVectorFunction gradient,
                double tol,
                int maxIterations)

Construct a Fletcher instance to minimize a function f.

Parameters:

rho - precision parameter; smaller rho gives better accuracy

sigma - precision parameter; smaller sigma gives better accuracy

tau - control parameter to avoid result too close to boundary

chi - control parameter to avoid result too close to boundary

f - the function to be minimized

gradient - the gradient of f

tol - the convergence tolerance. This affects the precision of the result.

maxIterations - the maximum number of iterations. This affects the precision of the result.

Fletcher

public Fletcher(RealScalarFunction f,
                RealVectorFunction gradient)

Construct a Fletcher instance to minimize a function f with the default control parameters.

Parameters:

f - the function to be minimized

gradient - the gradient of f

Method Detail

search

public double search(Vector x,
                     Vector d)

Get a so that f(x + a * d) is (approximately) minimized.

Parameters:

x - the initial position

d - the search direction

Returns:

a

See Also:

• "Algorithm 4.6. Practical Optimization: Algorithms and Engineering Applications. Andreas Antoniou, Wu-Sheng Lu."
• "Section 2.6. Practical Optimization: Algorithms and Engineering Applications. Andreas Antoniou, Wu-Sheng Lu."