org.ddogleg.optimization.impl

Class QuasiNewtonBFGS

java.lang.Object

org.ddogleg.optimization.impl.QuasiNewtonBFGS

public class QuasiNewtonBFGS
extends java.lang.Object

Quasi-Newton nonlinear optimization using BFGS update on the approximate inverse Hessian with a line search. The function and its gradient is required. If no gradient is available then a numerical gradient will be used. The line search must meet the Wolfe or strong Wolfe condition. This technique is automatically scale invariant and no scale matrix is required. In most situations super-linear convergence can be expected. Based on the description provided in [1].

The inverse Hessian update requires only a rank-2 making it efficient. Stability requires that the line search maintain the Wolfe or strong Wolfe condition or else the inverse Hessian matrix can stop being symmetric positive definite.

[1] Jorge Nocedal, Stephen J. Wright, "Numerical Optimization" 2nd Ed, 2006 Springer

Constructor Summary

Constructors

Constructor and Description
QuasiNewtonBFGS(GradientLineFunction function, LineSearch lineSearch, double funcMinValue) Configures the search.

Method Summary

Modifier and Type	Method and Description
double	getFx()
double[]	getParameters()
java.lang.String	getWarning() Returns the warning message, or null if there is none
void	initialize(double[] initial)
boolean	isConverged() True if the line search converged to a solution
boolean	isUpdatedParameters()
boolean	iterate() Perform one iteration in the optimization.
void	setConvergence(double ftol, double gtol, double lineGTol) Specify convergence tolerances
void	setInitialHInv(org.ejml.data.DenseMatrix64F Hinverse) Manually specify the initial inverse hessian approximation.

Methods inherited from class java.lang.Object

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

Constructor Detail

QuasiNewtonBFGS

public QuasiNewtonBFGS(GradientLineFunction function,
                       LineSearch lineSearch,
                       double funcMinValue)

Configures the search.

Parameters:

function - Function being optimized

lineSearch - Line search that selects a solution that meets the Wolfe condition.

funcMinValue - Minimum possible function value. E.g. 0 for least squares.

Method Detail

setConvergence

public void setConvergence(double ftol,
                           double gtol,
                           double lineGTol)

Specify convergence tolerances

Parameters:

ftol - Relative error tolerance for function value 0 <= ftol <= 1

gtol - Absolute convergence based on gradient norm 0 <= gtol

lineGTol - Slope coefficient for wolfe condition used in line search. 0 < lineGTol

setInitialHInv

public void setInitialHInv(org.ejml.data.DenseMatrix64F Hinverse)

Manually specify the initial inverse hessian approximation.

Parameters:

Hinverse - Initial hessian approximation

initialize

public void initialize(double[] initial)

getParameters

public double[] getParameters()

iterate

public boolean iterate()

Perform one iteration in the optimization.

Returns:

true if the optimization has stopped.

isConverged

public boolean isConverged()

True if the line search converged to a solution

getWarning

public java.lang.String getWarning()

Returns the warning message, or null if there is none

getFx

public double getFx()

isUpdatedParameters

public boolean isUpdatedParameters()