Package org.ddogleg.optimization.quasinewton

Class EquationsBFGS

java.lang.Object

org.ddogleg.optimization.quasinewton.EquationsBFGS

public class EquationsBFGS
extends 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	Description
EquationsBFGS()

Method Summary

Modifier and Type	Method	Description
static void	conjugateUpdateC(DMatrixRMaj C, DMatrixRMaj d, DMatrixRMaj y, double step, DMatrixRMaj tempV0, DMatrixRMaj tempV1)	[1] D.
static void	conjugateUpdateD(DMatrixRMaj C, DMatrixRMaj d, DMatrixRMaj y, double step, DMatrixRMaj tempV0)	[1] D.
static void	inverseUpdate(DMatrixRMaj H, DMatrixRMaj s, DMatrixRMaj y, DMatrixRMaj tempV0, DMatrixRMaj tempV1)	BFGS inverse hessian update equation that orders the multiplications to minimize the number of operations.
static void	update(DMatrixRMaj H, DMatrixRMaj s, DMatrixRMaj y, DMatrixRMaj tempV0, DMatrixRMaj tempV1)	DFP Hessian update equation.

Methods inherited from class java.lang.Object

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

Constructor Details

EquationsBFGS

public EquationsBFGS()

Method Details

update

public static void update(DMatrixRMaj H,
 DMatrixRMaj s,
 DMatrixRMaj y,
 DMatrixRMaj tempV0,
 DMatrixRMaj tempV1)

DFP Hessian update equation. See class description for equations

Parameters:

H - symmetric inverse matrix being updated

s - change in state (new - old)

y - change in gradient (new - old)

tempV0 - Storage vector

inverseUpdate

public static void inverseUpdate(DMatrixRMaj H,
 DMatrixRMaj s,
 DMatrixRMaj y,
 DMatrixRMaj tempV0,
 DMatrixRMaj tempV1)

BFGS inverse hessian 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(DMatrixRMaj C,
 DMatrixRMaj d,
 DMatrixRMaj y,
 double step,
 DMatrixRMaj 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(DMatrixRMaj C,
 DMatrixRMaj d,
 DMatrixRMaj y,
 double step,
 DMatrixRMaj tempV0,
 DMatrixRMaj 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