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Some numerical experiments with variable-storage quasi-Newton algorithms
Authors:Jean Charles Gilbert  Claude Lemaréchal
Institution:(1) International Institute for Applied Systems Analysis, A-2361 Laxenburg, Austria;(2) Present address: Institut National de Recherche en Informatique et en Automatique, F-78153 Le Chesnay, France
Abstract:This paper describes some numerical experiments with variable-storage quasi-Newton methods for the optimization of some large-scale models (coming from fluid mechanics and molecular biology). In addition to assessing these kinds of methods in real-life situations, we compare an algorithm of A. Buckley with a proposal by J. Nocedal. The latter seems generally superior, provided that careful attention is given to some nontrivial implementation aspects, which concern the general question of properly initializing a quasi-Newton matrix. In this context, we find it appropriate to use a diagonal matrix, generated by an update of the identity matrix, so as to fit the Rayleigh ellipsoid of the local Hessian in the direction of the change in the gradient.Also, a variational derivation of some rank one and rank two updates in Hilbert spaces is given.Work supported in part by FNRS (Fonds National de la Recherche Scientifique), Belgium.
Keywords:49D05  65K05
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