org.ddogleg.optimization.impl

Class EquationsBFGS

java.lang.Object

org.ddogleg.optimization.impl.EquationsBFGS

public class EquationsBFGS
extends java.lang.Object

Equations for updating the approximate Hessian matrix using BFGS equations.

Forward:

  B(k+1) = B(k) + [B(k)*s*s'*B(k)]/[s'*B*s]
                + y*y'/[y'*s]
 

Inverse:

  H(k+1) = (I-p*s*y')*H(k)*(I-p*y*s') + p*s*s'
 

• B = symmetric positive definite forward n by n matrix.
• H = symmetric positive definite inverse n by n matrix.
• s = x(k+1)-x(k) vector change in state.
• y = x'(k+1)-x'(k) vector change in gradient.
• p = 1/(y'*s) > 0

Constructor Summary

Constructors

Constructor and Description
EquationsBFGS()

Method Summary

Modifier and Type	Method and Description
static void	conjugateUpdateC(org.ejml.data.DenseMatrix64F C, org.ejml.data.DenseMatrix64F d, org.ejml.data.DenseMatrix64F y, double step, org.ejml.data.DenseMatrix64F tempV0, org.ejml.data.DenseMatrix64F tempV1) [1] D.
static void	conjugateUpdateD(org.ejml.data.DenseMatrix64F C, org.ejml.data.DenseMatrix64F d, org.ejml.data.DenseMatrix64F y, double step, org.ejml.data.DenseMatrix64F tempV0) [1] D.
static void	inverseUpdate(org.ejml.data.DenseMatrix64F H, org.ejml.data.DenseMatrix64F s, org.ejml.data.DenseMatrix64F y, org.ejml.data.DenseMatrix64F tempV0, org.ejml.data.DenseMatrix64F tempV1) Inverse update equation that orders the multiplications to minimize the number of operations.
static void	naiveInverseUpdate(org.ejml.data.DenseMatrix64F H, org.ejml.data.DenseMatrix64F s, org.ejml.data.DenseMatrix64F y) Naive but easy to visually verify implementation of the inverse BFGS update.

Methods inherited from class java.lang.Object

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

Constructor Detail

EquationsBFGS

public EquationsBFGS()

Method Detail

naiveInverseUpdate

public static void naiveInverseUpdate(org.ejml.data.DenseMatrix64F H,
                                      org.ejml.data.DenseMatrix64F s,
                                      org.ejml.data.DenseMatrix64F y)

Naive but easy to visually verify implementation of the inverse BFGS update. Primarily for testing purposes.

Parameters:

H - inverse matrix being updated

s - change in state

y - change in gradient

inverseUpdate

public static void inverseUpdate(org.ejml.data.DenseMatrix64F H,
                                 org.ejml.data.DenseMatrix64F s,
                                 org.ejml.data.DenseMatrix64F y,
                                 org.ejml.data.DenseMatrix64F tempV0,
                                 org.ejml.data.DenseMatrix64F tempV1)

Inverse update equation that orders the multiplications to minimize the number of operations.

Parameters:

H - symmetric inverse matrix being updated

s - change in state

y - change in gradient

tempV0 - Storage vector of length N

tempV1 - Storage vector of length N

conjugateUpdateD

public static void conjugateUpdateD(org.ejml.data.DenseMatrix64F C,
                                    org.ejml.data.DenseMatrix64F d,
                                    org.ejml.data.DenseMatrix64F y,
                                    double step,
                                    org.ejml.data.DenseMatrix64F tempV0)

[1] D. Byatt and I. D. Coope and C. J. Price, "Effect of limited precision on the BFGS quasi-Newton algorithm" Proc. of 11th Computational Techniques and Applications Conference CTAC-2003

Parameters:

C -

d -

y -

tempV0 -

conjugateUpdateC

public static void conjugateUpdateC(org.ejml.data.DenseMatrix64F C,
                                    org.ejml.data.DenseMatrix64F d,
                                    org.ejml.data.DenseMatrix64F y,
                                    double step,
                                    org.ejml.data.DenseMatrix64F tempV0,
                                    org.ejml.data.DenseMatrix64F tempV1)

[1] D. Byatt and I. D. Coope and C. J. Price, "Effect of limited precision on the BFGS quasi-Newton algorithm" Proc. of 11th Computational Techniques and Applications Conference CTAC-2003

Parameters:

C -

d -

y -

tempV0 -