com.numericalmethod.suanshu.optimization.unconstrained.quasinewton

Class QuasiNewton

java.lang.Object

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

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

All Implemented Interfaces:

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

Direct Known Subclasses:

BFGS, Huang

public abstract class QuasiNewton
extends SteepestDescent

The Quasi-Newton methods in optimization are for finding local maxima and minima of functions. The Quasi-Newton methods are based on Newton's method to find the stationary point of a function, where the gradient is 0. Newton's method assumes that the function can be locally approximated as quadratic in the region around the optimum. It uses the first and second derivatives (gradient and Hessian) to find the stationary point. In the Quasi-Newton methods the Hessian matrix of the objective function needs not to be computed. The Hessian is updated by analyzing successive gradient vectors instead.

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 7.2, 7.3," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Quasi-Newton method

, Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected class	QuasiNewton.QuasiNewtonImpl This is an implementation of the Quasi-Newton 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
QuasiNewton(double epsilon, int maxIterations) Construct a multivariate minimizer using a Quasi-Newton method.

Method Summary

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

solve

Methods inherited from class java.lang.Object

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

Constructor Detail

QuasiNewton

public QuasiNewton(double epsilon,
                   int maxIterations)

Construct a multivariate minimizer using a Quasi-Newton method.

Parameters:

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

maxIterations - the maximum number of iterations