Module hessian_update 

Hessian update methods (BFGS, Bofill, Powell) Hessian update methods for optimization algorithms.

This module implements various Hessian and inverse Hessian update formulas

Available Update Methods

• BFGS: Broyden-Fletcher-Goldfarb-Shanno for minima
• Bofill: Weighted Powell/Murtagh-Sargent for saddle points
• Powell: Symmetric rank-one update
• PSB: Powell-Symmetric-Broyden (legacy)

References

• Bofill, J. M. J. Comput. Chem. 1994, 15, 1-11.
• Powell, M. J. D. Math. Programming 1971, 1, 26-57.
• Murtagh, B. A.; Sargent, R. W. H. Comput. J. 1970, 13, 185-194.

Enums

HessianUpdateMethod

Hessian update method selection.

Constants

RMIN2 🔒

SMALL 🔒

Numerical thresholds for Hessian updates.

Functions

update_hessian_bfgs

BFGS Hessian update for minima (MthUpd=3).

update_hessian_bfgs_powell_mix

BFGS/Powell mixture following Bofill weighting.

update_hessian_bfgs_pure

Pure BFGS update without curvature check (MthUpd=5).

update_hessian_bofill

Bofill weighted update for saddle points.

update_hessian_powell

Powell symmetric rank-one update.

update_hessian_with_method

Updates the Hessian matrix using the specified method.

update_inverse_hessian_bfgs

Updates the inverse Hessian using BFGS formula.