Approximate invariant subspaces and quasi-Newton optimization methods

Serge Gratton; P.L. Toint

doi:10.1080/10556780902992746

Approximate invariant subspaces and quasi-Newton optimization methods

Serge Gratton, P.L. Toint

Résultats de recherche: Contribution à un journal/une revue › Article

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Résumé

New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples. © 2010 Taylor & Francis.

langue originale	Anglais
Pages (de - à)	507-529
Nombre de pages	23
journal	Optimization Methods and Software
Volume	25
Numéro de publication	4
Les DOIs	https://doi.org/10.1080/10556780902992746
état	Publié - 1 août 2010

Empreinte digitale

Quasi-Newton Method

Invariant Subspace

Optimization Methods

Chord or secant line

Newton-Raphson method

Unconstrained Minimization

Data storage equipment

Smoothing

Eigenvalue

Optimization

Dependent

Citer ceci

Gratton, S., & Toint, P. L. (2010). Approximate invariant subspaces and quasi-Newton optimization methods. Optimization Methods and Software, 25(4), 507-529. https://doi.org/10.1080/10556780902992746

Gratton, Serge ; Toint, P.L. / Approximate invariant subspaces and quasi-Newton optimization methods. Dans: Optimization Methods and Software. 2010 ; Vol 25, Numéro 4. p. 507-529.

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Gratton, S & Toint, PL 2010, 'Approximate invariant subspaces and quasi-Newton optimization methods', Optimization Methods and Software, VOL. 25, Numéro 4, p. 507-529. https://doi.org/10.1080/10556780902992746

Approximate invariant subspaces and quasi-Newton optimization methods. / Gratton, Serge; Toint, P.L.

Dans: Optimization Methods and Software, Vol 25, Numéro 4, 01.08.2010, p. 507-529.

Résultats de recherche: Contribution à un journal/une revue › Article

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