Some numerical experiments with variable-storage quasi-Newton algorithms - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Mathematical Programming Année : 1989

Some numerical experiments with variable-storage quasi-Newton algorithms

Résumé

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.
Fichier principal
Vignette du fichier
gilbert-lemarechal-1989.pdf (431.13 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY ND - Paternité - Pas de modifications

Dates et versions

hal-04135388 , version 1 (20-06-2023)

Licence

Paternité - Pas de modifications

Identifiants

Citer

Jean Charles Gilbert, Claude Lemaréchal. Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming, 1989, 45, pp.407-435. ⟨10.1007/BF01589113⟩. ⟨hal-04135388⟩

Collections

INRIA INRIA2
8 Consultations
50 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More