# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.optimization.multivariate.minmax

## Class LeastPth<T>

• java.lang.Object
• com.numericalmethod.suanshu.optimization.multivariate.minmax.LeastPth<T>
• All Implemented Interfaces:
MinMaxMinimizer<T>, Optimizer<MinMaxProblem<T>,IterativeSolution<Vector>>

public class LeastPth<T>
extends 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.

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

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

All Methods
Modifier and Type Method and Description
IterativeSolution<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 IterativeSolution<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>,IterativeSolution<Vector>>
Parameters:
problem - an optimization problem
Returns:
a solution to the optimization problem