Re: [Help-gsl] Comments/questions about BFGS algorithm implemented for the GSL

[Brian Gough]

Alan W. Irwin writes:
 > But why does it take so long (119 iterations) to get to the final rapid
 > convergence phase (both for the GSL C version and my fortran implementation
 > of the same algorithm)?  In Fletcher's book, "Practical Methods of
 > Optimization", 2nd edition, the problem only requires 21 iterations to
 > converge (see Table 3.5.1) with Fletcher's own BFGS code.  Although, my
 > experients showed the L-BFGS-B implementation is fundamentally non-robust,
 > for this test function it seems to be okay, and it converges in 39
 > iterations confirming there is something wrong with the efficiency of the
 > preliminary convergence steps in the GSL case.
 > 
 > I suspect there is a substantial inefficiency problem with the GSL line-
 > search implementation (since the BFGS update part is completely 
 > straightforward).  I am not any sort of expert in this field though so I
 > cannot pin down where the problem is occurring, but a superficial google
 > search reveals a number of complaints about the GSL minimization efficiency.

Thanks for your thoughtful comments.  I agree that the line
minimisation is a likely suspect and has room for improvement.  What
line minimisation method is used by Fletcher and what criteria for
stopping each line minimisation? (I don't have the book but I will see
about getting it).

-- 
Brian Gough

Network Theory Ltd,
Publishing the GSL Manual - http://www.network-theory.co.uk/gsl/manual/