Exploiting band structure in unconstrained optimization without derivatives

Benoit Colson; Philippe Toint

Exploiting band structure in unconstrained optimization without derivatives

Departement de mathematique

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

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 originale	Anglais
Pages (de - à)	399-412
Nombre de pages	14
journal	Optimization and Engineering
Numéro de publication	2
Etat de la publication	Publié - 2001

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Projets

2 Actif

DFO: Algorithmes d'optimisation numérique sans dérivées

TOINT, P., COLSON, B., Gratton, S., Tröltzsch, A. & RODRIGUES SAMPAIO, P.

1/03/94 → …

Projet: Recherche

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

SARTENAER, A. & TOINT, P.

1/01/87 → …

Projet: Axe de recherche

Thèses de l'étudiant

Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming

Author: Colson, B., 2003

Superviseur: Toint, P. (Promoteur), Henrard, J. (Jury), Sartenaer, A. (Jury), Savard, G. (Personne externe) (Jury) & VICENTE, L. (Personne externe) (Jury)

Thèse de l'étudiant: Doc types › Docteur en Sciences

Contient cette citation

Colson, B., & Toint, P. (2001). Exploiting band structure in unconstrained optimization without derivatives. Optimization and Engineering, (2), 399-412.

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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.",

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AB - 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.

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KW - sparsity

KW - trust-region methods

KW - derivative-free optimization

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