com.numericalmethod.suanshu.optimization.minmax

Class LeastPth<T>

java.lang.Object

com.numericalmethod.suanshu.optimization.minmax.LeastPth<T>

All Implemented Interfaces:

MinMaxMinimizer<T>, Optimizer<MinMaxProblem<T>,IterativeMinimizer<Vector>>, java.io.Serializable

public class LeastPth<T>
extends java.lang.Object
implements MinMaxMinimizer<T>

The least p-th minmax algorithm minimizes the maximal error/loss (function): \[ \min_x \max_{\omega \in S} e(x, \omega) \] \(e(x, \omega)\) is the error or loss function.

This implementation assumes the set S is discrete and finite. To use this to solve a continuous S set, a sampling of S is required.

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Algorithm 8.1.," Practical Optimization: Algorithms and Engineering Applications.", Serialized Form

Constructor Summary

Constructors

Constructor and Description
LeastPth(double epsilon, int maxIterations) Construct a minmax minimizer using the Least p-th method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(MinMaxProblem<T> 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

LeastPth

public LeastPth(double epsilon,
                int maxIterations)

Construct a minmax minimizer using the Least p-th 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(MinMaxProblem<T> problem)

Description copied from interface: Optimizer

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

Specified by:

solve in interface Optimizer<MinMaxProblem<T>,IterativeMinimizer<Vector>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem