Some numerical experiments with variable-storage quasi-Newton algorithms

Gilbert, J.-C. & Lemarechal, C. (1989). Some numerical experiments with variable-storage quasi-Newton algorithms. Mathematical Programming 45 (1-3) 407-435. 10.1007/BF01589113.

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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

Item Type: Article
Uncontrolled Keywords: Conjugate gradient; diagonal updates; Hilbert spaces; large-scale problems; limited memory; numerical experiments; unconstrained optimization; variable-metric algorithms; variablestorage
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: Romeo Molina
Date Deposited: 19 Apr 2016 09:24
Last Modified: 27 Aug 2021 17:26

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