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Re: Proposition of a better convergion criterion in multimin
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Philippe Huber <huberph at infomaniak dot ch>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Mon, 26 Aug 2002 21:09:39 +0100 (BST)
- Subject: Re: Proposition of a better convergion criterion in multimin
- References: <000001c248f6$e7394500$7e28c281@osiris>
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.