com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection

Class Powell

java.lang.Object

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

com.numericalmethod.suanshu.optimization.unconstrained.conjugatedirection.Powell

All Implemented Interfaces:

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

public class Powell
extends SteepestDescent

Powell's algorithm, starting from an initial point, performs a series of line searches in one iteration. The line search directions, except the last one, are all linearly independent. The major advantage of Powell’s algorithm is that the Hessian needs not be supplied, stored or manipulated. However, this algorithm has a few drawbacks and is superseded by Zangwill’s algorithm. For example, in an iteration, linear dependence can sometimes arise, which may fail to find complete the set of linearly independent directions that span Eⁿ, even in the case of a convex quadratic problem.

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "Theorem 6.5, Algorithm 6.4," Practical Optimization: Algorithms and Engineering Applications.", Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected class	Powell.PowellImpl an implementation of Powell'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
Powell(double epsilon, int maxIterations) Construct a multivariate minimizer using the Powell 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

Powell

public Powell(double epsilon,
              int maxIterations)

Construct a multivariate minimizer using the Powell method.

Parameters:

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

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