Re: Proposition of a better convergion criterion in multimin

[Brian Gough <bjg@network-theory.co.uk>]

Philippe Huber writes:
 >  I found that the stopping criterion proposed in
 > gsl_multimin_test_gradient suffers from scale problems. Typically,
 > if you have variables of magnitude 1.0e0 and a function of
 > magnitude 1.0e5, it can be impossible to minimize the norm of the
 > gradient under 1.0e-2.  Dennis and Schnabel in "Numerical Methods
 > for Unconstrained Optimization and Nonlinear Equations", p.160
 > propose another criterion: relgrad = gradfi * xi / f, where gradfi
 > is the ith component of the gradient and xi the ith variable. The
 > criterion is ||relgrad||inf < epsabs, with ||.||inf is the infinite
 > norm: ||x||inf=max(|xi|).  Here is a proposition of a new routine
 > called gsl_multimin_test_relgrad:

How about scaling the components of g? This would be invariant under
x->x+constant, f->f+constant which seems like a useful property.