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[Bug-gsl] [bug #45099] wrong formula for BFGS update in gsl_multimin?

From: Patrick Alken
Subject: [Bug-gsl] [bug #45099] wrong formula for BFGS update in gsl_multimin?
Date: Wed, 13 May 2015 15:03:15 +0000
User-agent: Mozilla/5.0 (X11; Linux i686 on x86_64; rv:37.0) Gecko/20100101 Firefox/37.0


                 Summary: wrong formula for BFGS update in gsl_multimin?
                 Project: GNU Scientific Library
            Submitted by: psa
            Submitted on: Wed 13 May 2015 03:03:13 PM GMT
                Category: None
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
         Discussion Lock: Any



>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?




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