com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent

Class GaussNewton

java.lang.Object

com.numericalmethod.suanshu.optimization.unconstrained.steepestdescent.GaussNewton

public class GaussNewton
extends java.lang.Object

The Gauss-Newton method is a steepest descent method to minimize a real vector function in the form: /[ f(x) = [f_1(x), f_2(x), ..., f_m(x)]' /] The objective function is /[ F(x) = f' %*% f ]/

See Also:

• "Andreas Antoniou, Wu-Sheng Lu, "Algorithm 5.5," Practical Optimization: Algorithms and Engineering Applications."
• Wikipedia: Gauss–Newton algorithm

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
protected static class	GaussNewton.MySteepestDescent

Constructor Summary

Constructors

Constructor and Description
GaussNewton(double epsilon, int maxIterations) Construct a multivariate minimizer using the Gauss-Newton method.

Method Summary

Modifier and Type	Method and Description
IterativeMinimizer<Vector>	solve(RealVectorFunction vf) Solve the minimization problem to minimize F = vf' * vf.
IterativeMinimizer<Vector>	solve(RealVectorFunction vf, RntoMatrix J) Solve the minimization problem to minimize F = vf' * vf.

Methods inherited from class java.lang.Object

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

Constructor Detail

GaussNewton

public GaussNewton(double epsilon,
                   int maxIterations)

Construct a multivariate minimizer using the Gauss-Newton method.

Parameters:

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

maxIterations - the maximum number of iterations

Method Detail

solve

public IterativeMinimizer<Vector> solve(RealVectorFunction vf,
                                        RntoMatrix J)
                                 throws java.lang.Exception

Solve the minimization problem to minimize F = vf' * vf.

Parameters:

vf - a real vector function to be minimized

J - a function that computes the Jacobian of f for a given x

Returns:

a minimizer

Throws:

java.lang.Exception

solve

public IterativeMinimizer<Vector> solve(RealVectorFunction vf)
                                 throws java.lang.Exception

Solve the minimization problem to minimize F = vf' * vf.

Parameters:

vf - a real vector function to be minimized

Returns:

a minimizer

Throws:

java.lang.Exception