bugGNU Scientific Library - Bugs: bug #45099, wrong formula for BFGS update in...


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bug #45099: wrong formula for BFGS update in gsl_multimin?

Submitter:  Patrick Alken <psa>
Submitted:  Wed 13 May 2015 03:03:13 PM UTC
Category:  None Severity:  3 - Normal
Operating System:  Status:  None
Assigned to:  None Open/Closed:  Open

Wed 13 May 2015 03:03:13 PM UTC, original submission:  

From Clayton =dot= Davis =at= nrl =dot= navy =dot= mil

There was another email sent to this list two years ago by Martin:  http://lists.gnu.org/archive/html/bug-gsl/2013-04/msg00002.html.  In his email, he raised a concern about the BFGS multimin implementations (both gsl_multimin_fdfminimizer_vector_bfgs and gsl_multimin_fdfminimizer_vector_bfgs2); I would like to second the concern.

Essentially, the concern boils down to this: BFGS search is supposed to build an approximation of the hessian of the function over successive iterations.  In any implementation I'm aware of, that approximate hessian should be stored explicitly.  In GSL's implementations, however, it is nowhere to be found; Martin suspected two years ago, and I agree, that the hessian seems to be treated as an identity matrix with no updates.  If that is true, it would be a serious implementation flaw in these functions.

Does anyone have any insight into this?



Patrick Alken <psa>
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