Mathematical Programming

, Volume 45, Issue 1, pp 407–435

Some numerical experiments with variable-storage quasi-Newton algorithms

  • Jean Charles Gilbert
  • Claude Lemaréchal

DOI: 10.1007/BF01589113

Cite this article as:
Gilbert, J.C. & Lemaréchal, C. Mathematical Programming (1989) 45: 407. doi:10.1007/BF01589113


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.

AMS (MOS) Subject Classifications

49D05 65K05 

Key words

Conjugate gradient diagonal updates Hilbert spaces large-scale problems limited memory numerical experiments unconstrained optimization variable-metric algorithms variablestorage 

Copyright information

© North-Holland 1989

Authors and Affiliations

  • Jean Charles Gilbert
    • 1
  • Claude Lemaréchal
    • 2
  1. 1.International Institute for Applied Systems AnalysisLaxenburgAustria
  2. 2.Institut National de Recherche en Informatique et en AutomatiqueLe ChesnayFrance

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