Exploiting band structure in unconstrained optimization without derivatives

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

Cet article traite de l'optimisation sans contraintes et sans dérivées. Nous présentons d'abord une méthode combinant l'utilisation de polynômes d'interpolation et des techniques de régions de confiance pour minimiser une fonction dont les dérivées ne sont pas disponibles. Nous montrons ensuite comment l'algorithme qui en résulte peut être adapté d'une façon pertinente pour considérer des problèmes dont la matrice Hessienne est creuse. Des résultats numériques confirment le bon comportement de la méthode et en particulier les avantages qu'elle présente en termes de stockage, évaluations de fonctions et vitesse d'exécution.
langue originaleAnglais
Pages (de - à)399-412
Nombre de pages14
journalOptimization and Engineering
Numéro de publication2
étatPublié - 2001

Empreinte digitale

Band Structure
Unconstrained Optimization
Band structure
Derivative-free Optimization
Derivatives
Derivative
Trust Region
Hessian matrix
Function evaluation
Polynomial Interpolation
Evaluation Function
Interpolation
Numerical Experiment
Polynomials
Minimise
Experiments

Citer ceci

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title = "Exploiting band structure in unconstrained optimization without derivatives",
abstract = "This paper is concerned with derivative-free unconstrained optimization. We first discuss a method combining the use of interpolation polynomials and trust-region techniques to minimize a function whose derivatives are not available. We then show how the resulting algorithm may be adapted in a suitable way to consider problems for which the Hessian matrix is known to be sparse. Numerical experiments confirm the favourable behaviour of the method and in particular the advantages in terms of storage, function evaluations and speed.",
keywords = "interpolation models, sparsity, trust-region methods, derivative-free optimization",
author = "Benoit Colson and Philippe Toint",
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Exploiting band structure in unconstrained optimization without derivatives. / Colson, Benoit; Toint, Philippe.

Dans: Optimization and Engineering, Numéro 2, 2001, p. 399-412.

Résultats de recherche: Contribution à un journal/une revueArticle

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