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

[Clayton Davis]

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?



Thanks,

Clayton