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, UnconstrainedMinimizer

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 function to be minimized needs not to be computed. The Hessian is updated by analyzing successive gradient vectors instead.

See Also:

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

Nested Class Summary

class

QuasiNewton.QuasiNewtonImpl An implementation of the Quasi-Newton algorithm.

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

QuasiNewton()

Method Summary

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

getLineSearch, minimum, search, solve, solve, solve

Methods inherited from class java.lang.Object

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

Constructor Detail

QuasiNewton

public QuasiNewton()