com.numericalmethod.suanshu.optimization.unconstrained.quasinewton

Class DFP

java.lang.Object

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

com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.QuasiNewton

com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.Huang

com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.DFP

All Implemented Interfaces:

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

public class DFP
extends Huang

The Davidon-Fletcher-Powell method is a quasi-Newton method to solve unconstrained nonlinear optimization problems. This method maintains the symmetry and positive definiteness of the Hessian matrix.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Section 7.5, Table 7.1," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Davidon–Fletcher–Powell formula

, Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.Huang

Huang.HuangImpl

Nested classes/interfaces inherited from class com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.QuasiNewton

QuasiNewton.QuasiNewtonImpl

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
DFP(double epsilon, int maxIterations) Construct a multivariate minimizer using the DFP method.

Method Summary

Modifier and Type	Method and Description
static Matrix	updateHessianInverse(Matrix S, Matrix gamma, Matrix delta) Sk+1 = Sk + δδ' / γ'δ - Sγγ'S' / γ'Sγ

Methods inherited from class com.numericalmethod.suanshu.optimization.unconstrained.quasinewton.Huang

solve

Methods inherited from class java.lang.Object

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

Constructor Detail

DFP

public DFP(double epsilon,
           int maxIterations)

Construct a multivariate minimizer using the DFP method.

Parameters:

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

maxIterations - the maximum number of iterations

Method Detail

updateHessianInverse

public static Matrix updateHessianInverse(Matrix S,
                                          Matrix gamma,
                                          Matrix delta)

S_k+1 = S_k + δδ' / γ'δ - Sγγ'S' / γ'Sγ

Parameters:

S - the inverse of a Hessian

gamma - γ

delta - δ

Returns:

an updated Hessian matrix

See Also:

"Andreas Antoniou, Wu-Sheng Lu, "eq. 7.29," Practical Optimization: Algorithms and Engineering Applications."