com.numericalmethod.suanshu.optimization.unconstrained.quasinewton

Class QuasiNewton.QuasiNewtonImpl

java.lang.Object

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

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

All Implemented Interfaces:

IterativeMethod<Vector>, IterativeMinimizer<Vector>, MinimizationSolution<Vector>, java.io.Serializable

Direct Known Subclasses:

BFGS.BFGSImpl, Huang.HuangImpl

Enclosing class:

QuasiNewton

protected abstract class QuasiNewton.QuasiNewtonImpl
extends SteepestDescent.SteepestDescentImpl

This is an implementation of the Quasi-Newton algorithm. A sub-class supplies the Hessian updating rule.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
protected double	ak the increment in the search direction
protected Vector	dk the line search direction at the k-th iteration
protected Vector	gk the gradient at the k-th iteration
protected Matrix	Sk This is the approximate inverse of the Hessian matrix.

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

linesearch, problem

Method Summary

Modifier and Type	Method and Description
Vector	getDirection(Vector xk) Get the next search direction.
double	getIncrement(Vector xk, Vector dk) Get the increment fraction, αk.

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

minimizer, minimum, search, setInitials, step

Methods inherited from class java.lang.Object

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

Field Detail

Sk

protected Matrix Sk

This is the approximate inverse of the Hessian matrix. An implementation of updateSk(com.numericalmethod.suanshu.vector.doubles.Vector) modifies this incrementally.

gk

protected Vector gk

the gradient at the k-th iteration

dk

protected Vector dk

the line search direction at the k-th iteration

ak

protected double ak

the increment in the search direction

Method Detail

getDirection

public Vector getDirection(Vector xk)

Description copied from class: SteepestDescent.SteepestDescentImpl

Get the next search direction.

Specified by:

getDirection in class SteepestDescent.SteepestDescentImpl

Parameters:

xk - the current minimizer

Returns:

the next search direction

getIncrement

public double getIncrement(Vector xk,
                           Vector dk)

Description copied from class: SteepestDescent.SteepestDescentImpl

Get the increment fraction, α_k.

Overrides:

getIncrement in class SteepestDescent.SteepestDescentImpl

Parameters:

xk - the current minimizer

dk - the search direction

Returns:

α_k