From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 6118 invoked by alias); 26 Aug 2002 20:12:14 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 6108 invoked from network); 26 Aug 2002 20:12:13 -0000 Received: from unknown (HELO blueyonder.co.uk) (195.188.53.96) by sources.redhat.com with SMTP; 26 Aug 2002 20:12:13 -0000 Received: from pcow053o.blueyonder.co.uk ([127.0.0.1]) by blueyonder.co.uk with Microsoft SMTPSVC(5.5.1877.757.75); Mon, 26 Aug 2002 21:12:06 +0100 Received: from localhost (unverified [80.192.11.48]) by pcow053o.blueyonder.co.uk (Content Technologies SMTPRS 4.2.9) with ESMTP id ; Mon, 26 Aug 2002 21:09:47 +0100 Received: by network-theory.co.uk via sendmail from stdin id (Debian Smail3.2.0.102) for huberph@infomaniak.ch; Mon, 26 Aug 2002 21:09:39 +0100 (BST) From: Brian Gough MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit Message-ID: <15722.35587.116438.176395@debian> Date: Mon, 26 Aug 2002 13:12:00 -0000 To: Philippe Huber Cc: gsl-discuss@sources.redhat.com Subject: Re: Proposition of a better convergion criterion in multimin In-Reply-To: <000001c248f6$e7394500$7e28c281@osiris> References: <000001c248f6$e7394500$7e28c281@osiris> X-SW-Source: 2002-q3/txt/msg00174.txt.bz2 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.