com.numericalmethod.suanshu.optimization.constrained.general.penaltymethod

Class PenaltyMethodMinimizer

java.lang.Object

com.numericalmethod.suanshu.optimization.constrained.general.penaltymethod.PenaltyMethodMinimizer

All Implemented Interfaces:

ConstrainedMinimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, Minimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, Optimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>, java.io.Serializable

public class PenaltyMethodMinimizer
extends java.lang.Object
implements ConstrainedMinimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>

The penalty method is an algorithm for solving a constrained minimization problem with general constraints. It replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The unconstrained problems are formed by adding a term to the objective function that consists of a penalty parameter and a measure of violation of the constraints. The measure of violation is zero in the feasible region and is positive when the constraints are violated.

In this implementation, we use only one iteration. In this iteration, we multiply the penalties by ɣ, which is a very big number, to penalize a solution outside the feasible region. This is to mimic when ɣ approaches infinity. A classical unconstrained minimization algorithm is then applied to the modified problem. It can be shown that if the penalty is large enough, the original and modified problems have the same solution.

See Also:

• @see Wikipedia: Penalty method
• "R. Fletcher, "Section 22.4, Penalty Methods, Chapter 22, Non-differentiable Optimization," Practical Methods of Optimization. 2nd ed. Wiley. May 2000."

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	PenaltyMethodMinimizer.PenaltyFunctionFactory For each constrained optimization problem, the solver creates a new penalty function for it.

Field Summary

Fields

Modifier and Type	Field and Description
static PenaltyMethodMinimizer.PenaltyFunctionFactory	DEFAULT_PENALTY_FUNCTION_FACTORY the default penalty function factory

Constructor Summary

Constructors

Constructor and Description
PenaltyMethodMinimizer() Construct a constrained minimizer using the penalty method.
PenaltyMethodMinimizer(double gamma) Construct a constrained minimizer using the penalty method.
PenaltyMethodMinimizer(PenaltyMethodMinimizer.PenaltyFunctionFactory penaltyFunctionFactory, double gamma, T minimizer) Construct a constrained minimizer using the penalty method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(ConstrainedOptimProblem 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

Field Detail

DEFAULT_PENALTY_FUNCTION_FACTORY

public static final PenaltyMethodMinimizer.PenaltyFunctionFactory DEFAULT_PENALTY_FUNCTION_FACTORY

the default penalty function factory

Constructor Detail

PenaltyMethodMinimizer

public PenaltyMethodMinimizer(PenaltyMethodMinimizer.PenaltyFunctionFactory penaltyFunctionFactory,
                              double gamma,
                              T minimizer)

Construct a constrained minimizer using the penalty method.

Type Parameters:

T - a multivariate, iterative minimizer type

Parameters:

penaltyFunctionFactory - a factory to construct a penalty function from a constrained optimization problem

gamma - the ɣ as in R. Fletcher

minimizer - an unconstrained minimization solver

PenaltyMethodMinimizer

public PenaltyMethodMinimizer(double gamma)

Construct a constrained minimizer using the penalty method. ɣ should be big enough to reflect the penalty, but it cannot be too big to overflow the computations (to produce NaNs). It is recommended to experiment different ɣ's to get better results.

Parameters:

gamma - the ɣ as in R. Fletcher

PenaltyMethodMinimizer

public PenaltyMethodMinimizer()

Construct a constrained minimizer using the penalty method.

Method Detail

solve

public IterativeMinimizer<Vector> solve(ConstrainedOptimProblem problem)
                                 throws java.lang.Exception

Description copied from interface: Optimizer

Solve an optimization problem, e.g., OptimProblem.

Specified by:

solve in interface Optimizer<ConstrainedOptimProblem,IterativeMinimizer<Vector>>

Parameters:

problem - an optimization problem

Returns:

a solution to the optimization problem

Throws:

java.lang.Exception - when there is an error solving the problem