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, UnconstrainedMinimizer

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.

A conjugate direction optimization method is performed by using sequential search directions that bear a strict mathematical relationship to one another.

See Also:

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

Nested Class Summary

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

SteepestDescent.LineSearch

Field Summary

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

f, g, tol

Constructor Summary

Zangwill()

Method Summary

protected SteepestDescent.LineSearch	getLineSearch()
void	solve(RealScalarFunction f, RealVectorFunction g, double tol) Construct an instance of Zangwill to minimize a function.
void	solve(RealScalarFunction f, RealVectorFunction g, double tol, double tol2) Solve an instance of Zangwill to minimize a function f.

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

minimum, search, solve, solve

Methods inherited from class java.lang.Object

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

Constructor Detail

Zangwill

public Zangwill()

Method Detail

solve

public void solve(RealScalarFunction f,
                  RealVectorFunction g,
                  double tol,
                  double tol2)

Solve an instance of Zangwill to minimize a function f.

Parameters:

f - the real valued function to be minimized

g - a function that computes the gradient of f for a given x

tol - the convergence tolerance

tol2 - a tolerance to decide whether there is linear dependence among the conjugate directions

solve

public void solve(RealScalarFunction f,
                  RealVectorFunction g,
                  double tol)

Construct an instance of Zangwill to minimize a function.

Overrides:

solve in class SteepestDescent

Parameters:

f - the real valued function to be minimized

g - a function that computes the gradient of f for a given x

tol - the convergence tolerance

getLineSearch

protected SteepestDescent.LineSearch getLineSearch()

Specified by:

getLineSearch in class SteepestDescent