com.numericalmethod.suanshu.optimization.unconstrained

Class NelderMead

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.NelderMead

All Implemented Interfaces:

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

public class NelderMead
extends java.lang.Object
implements MultivariateMinimizer<IterativeMinimizer<Vector>>

The Nelder–Mead method is a nonlinear optimization technique, which is well-defined for twice differentiable and unimodal problems. It starts with a simplex, and then uses operations reflection, expansion, contraction, and reduction to search for the minimum/maximum point. However, the Nelder–Mead technique is only a heuristic, since it can converge to non-stationary points on problems that can be solved by alternative methods. It does not always converge even for smooth problems. In practice, however, the performance is generally good. Note that one dimensional optimization by Nelder-Mead is unreliable.

See Also:

Wikipedia: Nelder–Mead method, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	NelderMead.Solution This is the solution to an optimization problem by the Nelder-Mead method.

Constructor Summary

Constructors

Constructor and Description
NelderMead(double alpha, double gamma, double rho, double sigma, double epsilon, int maxIterations) Construct a Nelder-Mead multivariate minimizer.
NelderMead(double epsilon, int maxIterations) Construct a Nelder-Mead multivariate minimizer.

Method Summary

Modifier and Type	Method and Description
NelderMead.Solution	solve(C2OptimProblem problem) Solve an optimization problem, e.g., OptimProblem.

Methods inherited from class java.lang.Object

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

Constructor Detail

NelderMead

public NelderMead(double alpha,
                  double gamma,
                  double rho,
                  double sigma,
                  double epsilon,
                  int maxIterations)

Construct a Nelder-Mead multivariate minimizer.

Parameters:

alpha - the reflection coefficient

gamma - the shrink/reduction coefficient

rho - the contraction coefficient

sigma - the shrink/reduction coefficient

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

maxIterations - the maximum number of iterations

NelderMead

public NelderMead(double epsilon,
                  int maxIterations)

Construct a Nelder-Mead multivariate minimizer.

Parameters:

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

maxIterations - the maximum number of iterations

Method Detail

solve

public NelderMead.Solution solve(C2OptimProblem problem)

Description copied from interface: Optimizer

Solve an optimization problem, e.g., OptimProblem.

Specified by:

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

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem