SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.optimization.multivariate.minmax

Interface MinMaxProblem<T>

• public interface MinMaxProblem<T>
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.
Wikipedia: Minimax
• Method Summary

All Methods
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.
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)

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:
gω(x), the gradient of the absolute error for a given ω
• getOmega

List<T> getOmega()
Get the list of omegas, the domain.
Returns:
the set of omegas