com.numericalmethod.suanshu.optimization.minmax
Class LeastPth

java.lang.Object
  com.numericalmethod.suanshu.optimization.minmax.LeastPth

public class LeastPth
extends java.lang.Object

The least p-th minmax algorithm solves the minmax problem in this form:

 minimize max e(x, ω)
    x     ω∈S 
 

e(x, ω) is the error or loss function.

In other words, the objective of the minmax algorithm is to minimize the maximal error/loss (function).

The least p-th minmax algorithm assumes the set S is discrete and finite. To use this implementation to solve a continuous S set, a sampling of S is required.

See Also:

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

Field Summary

MinMaxProblem

problem the minmax problem to be solved

Constructor Summary

LeastPth(MinMaxProblem problem)
Construct an instance of the LeastPth to solve a minmax problem.

Method Summary

Vector

search(Vector initial, java.util.List<java.lang.Object> omegas, double threshold, int maxIterations) Search for a minmax solution.

Methods inherited from class java.lang.Object

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

Field Detail

problem

public final MinMaxProblem problem

the minmax problem to be solved

Constructor Detail

LeastPth

public LeastPth(MinMaxProblem problem)

Construct an instance of the LeastPth to solve a minmax problem.

Parameters:

problem - the minmax problem to be solved

Method Detail

search

public Vector search(Vector initial,
                     java.util.List<java.lang.Object> omegas,
                     double threshold,
                     int maxIterations)

Search for a minmax solution.

Parameters:

initial - an initial guess of the minimizer

omegas - the S set

threshold - the convergence criterion

maxIterations - the maximum number of iterations

Returns:

an approximate minimizer/solution for the minmax problem