com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection

Class Zangwill

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.Zangwill

All Implemented Interfaces:

Minimizer<C2OptimProblem,IterativeMinimizer<Vector>>, Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>, MultivariateMinimizer<IterativeMinimizer<Vector>>, java.io.Serializable

public class Zangwill
extends SteepestDescent

Zangwill's algorithm is an improved version of Powell's algorithm. It enhances the algorithm to generate a set of conjugate directions that are always linearly independent. Despite the "improvement", in practice however, Zangwill's algorithm seems to produce results that are less accurate than those of Powell's algorithm.

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Algorithm 6.5," Practical Optimization: Algorithms and Engineering Applications.", Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected class	Zangwill.ZangwillImpl an implementation of Zangwill's algorithm

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

SteepestDescent.SteepestDescentImpl

Field Summary

Fields inherited from class com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.SteepestDescent

epsilon, maxIterations

Constructor Summary

Constructors

Constructor and Description
Zangwill(double epsilon, double epsilon2, int maxIterations) Construct a multivariate minimizer using the Zangwill method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(C2OptimProblem problem) Solve a minimization problem with a C2 objective function.

Methods inherited from class java.lang.Object

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

Constructor Detail

Zangwill

public Zangwill(double epsilon,
                double epsilon2,
                int maxIterations)

Construct a multivariate minimizer using the Zangwill method.

Parameters:

epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0

epsilon2 - a precision parameter to decide whether there is a linear dependence among the conjugate directions

maxIterations - the maximum number of iterations

Method Detail

solve

public IterativeMinimizer<Vector> solve(C2OptimProblem problem)
                                 throws java.lang.Exception

Description copied from class: SteepestDescent

Solve a minimization problem with a C² objective function.

Specified by:

solve in interface Optimizer<C2OptimProblem,IterativeMinimizer<Vector>>

Specified by:

solve in class SteepestDescent

Parameters:

problem - a minimization problem with a C² objective function

Returns:

a minimizer

Throws:

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