com.numericalmethod.suanshu.optimization.minmax
Class MinMaxProblem

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

public class MinMaxProblem
extends java.lang.Object

This class defines a minmax problem. It 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 the family of error functions, parameterized by omega, we try to minimize their maximum.

If the analytical form of the gradient of the absolute errors is available, the user should provide it. Otherwise, the numerical gradient is used.

See Also:

Wikipedia: Minimax

Nested Class Summary

static interface	MinMaxProblem.Error e(x, ω): the minmax objective function family, parameterized by omega
static interface	MinMaxProblem.Gradient the gradient of the absolute minmax objective function, for a given ω

Field Summary

MinMaxProblem.Error	error the minmax objective function e(x, ω)
MinMaxProblem.Gradient	gradient the gradient of the absolute value of the minmax objective function, for a given ω

Constructor Summary

MinMaxProblem(MinMaxProblem.Error error)
Construct a minmax problem, from an objective (error) function.

MinMaxProblem(MinMaxProblem.Error error, MinMaxProblem.Gradient gradient)
Construct a minmax problem, from an objective (error) function and the gradient of its absolute value.

Method Summary

Methods inherited from class java.lang.Object

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

Field Detail

error

public final MinMaxProblem.Error error

the minmax objective function e(x, ω)

gradient

public final MinMaxProblem.Gradient gradient

the gradient of the absolute value of the minmax objective function, for a given ω

Constructor Detail

MinMaxProblem

public MinMaxProblem(MinMaxProblem.Error error,
                     MinMaxProblem.Gradient gradient)

Construct a minmax problem, from an objective (error) function and the gradient of its absolute value.

Parameters:

error - the objective function

gradient - the gradient of the absolute value of the objective function

MinMaxProblem

public MinMaxProblem(MinMaxProblem.Error error)

Construct a minmax problem, from an objective (error) function.

The problem is solved using a numerical gradient.

Parameters:

error - the objective function of the minmax problem