com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection

Class FletcherReeves

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.ConjugateGradient

com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.FletcherReeves

All Implemented Interfaces:

Minimizer<C2OptimProblem,IterativeMinimizer<Vector>>, Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>, MultivariateMinimizer<IterativeMinimizer<Vector>>, java.io.Serializable

public class FletcherReeves
extends ConjugateGradient

The Fletcher-Reeves method is a variant of the Conjugate-Gradient method. Instead of finding the minimizer along a direction using an analytical formula as in ConjugateGradient, it uses a line search. The advantages are:

• The modification renders the method more amenable to the minimization of non-quadratic problems since a larger reduction can be achieved in f(x) along d_k at points outside the neighborhood of the solution.
• The modification does not compute the Hessian.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 6.3," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Conjugate gradient method

, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

SteepestDescent.SteepestDescentImpl

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

epsilon, maxIterations

Constructor Summary

Constructors

Constructor and Description
FletcherReeves(double epsilon, int maxIterations) Construct a multivariate minimizer using the Fletcher-Reeves method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(C2OptimProblem problem) Solve a minimization problem with a C2 objective function.

Methods inherited from class java.lang.Object

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

Constructor Detail

FletcherReeves

public FletcherReeves(double epsilon,
                      int maxIterations)

Construct a multivariate minimizer using the Fletcher-Reeves method.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

maxIterations - the maximum number of iterations

Method Detail

solve

public IterativeMinimizer<Vector> solve(C2OptimProblem problem)
                                 throws java.lang.Exception

Description copied from class: SteepestDescent

Solve a minimization problem with a C² objective function.

Specified by:

solve in interface Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>

Overrides:

solve in class ConjugateGradient

Parameters:

problem - a minimization problem with a C² objective function

Returns:

a minimizer

Throws:

java.lang.Exception - when there is an error solving the problem