Subject: BFGS vs. DFP

From: [email-masked] (Folke Noertemann)
Date: Wed, 15 Jul 1998 17:56:36 +0200

Dear CCL'ers,

 I have a question concerning the update algorithms used for the Hessian
during optimizations and transition state searches.
In a paper by J.Baker (J.Comp.Chem 7, 385-395 (1986)) and some manuals (Gamess, Gaussian) 
the statement is made that while the BFGS update is *better* for an
optimization, for a transition state search the DFP update is to be preferred. 
Of course, no reason is provided to support this statement.
One of the books frequently referred to (Fletcher: Practical
Methods of Optimization) makes the following statements: 
- Provided that the function being optimized is quadratic AND the line-search
  is exact, positive definiteness of the Hessian is preserved
  (for both DFP and BFGS formulas)
- For inexact line searches, global convergence of the BFGS method has been 
  proved.
  However, for the DFP this could not be shown.

Is this somehow related to the fact that for TS searches, the DFP-method is
recommended? Why is this so? Does this mean that the BFGS method will 
lead to a positive-definite Hessian, even if the the initial Hessian
has the required negative eigenvalue ?

Any hint is appreciated!

Thanks,
 F. Noertemann

Folke Noerteman
Lehrstuhl f. Theoret. Chemie
TU Muenchen
[email-masked]