com.numericalmethod.suanshu.optimization.minmax

Interface MinMaxProblem<T>

All Superinterfaces:

java.io.Serializable

public interface MinMaxProblem<T>
extends java.io.Serializable

A minmax problem is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss while maximizing the potential gain. Alternatively, it can be thought of as maximizing the minimum gain (maxmin). Given a family of error functions, parameterized by ω, we try to minimize their maximum.

See Also:

Wikipedia: Minimax

Method Summary

Modifier and Type	Method and Description
RealScalarFunction	error(T omega) e(x, ω) is the error function, or the minmax objective, for a given ω.
java.util.List<T>	getOmega() Get the list of omegas, the domain.
RealVectorFunction	gradient(T omega) g(x, ω) = ∇|e(x, ω)| is the gradient function of the absolute error, |e(x, ω)|, for a given ω.

Method Detail

error

RealScalarFunction error(T omega)

e(x, ω) is the error function, or the minmax objective, for a given ω.

Parameters:

omega - a parameterization of a real scalar function

Returns:

the error function for a given ω, e(x, ω)

gradient

RealVectorFunction gradient(T omega)

g(x, ω) = ∇|e(x, ω)| is the gradient function of the absolute error, |e(x, ω)|, for a given ω.

Parameters:

omega - a parameterization of a real scalar function

Returns:

g_ω(x), the gradient of the absolute error for a given ω

getOmega

java.util.List<T> getOmega()

Get the list of omegas, the domain.

Returns:

the set of omegas