Exploiting band structure in unconstrained optimization without derivatives

Benoit Colson; Philippe Toint

Exploiting band structure in unconstrained optimization without derivatives

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

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

1 Article

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables
Porcelli, M. & Toint, P., 30 juin 2017, Dans: Transactions of the American Methematical Society on Mathematical Software. 44, 1, 28 p., 6.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

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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

Trust-region algorithms for derivative-free optimization and nonlinear bilevel programming
Auteur: Colson, B., 2003
Superviseur: Toint, P. (Promoteur), Henrard, J. (Jury), Sartenaer, A. (Jury), Savard, G. (Personne externe) (Jury) & VICENTE, L. (Personne externe) (Jury)
Student thesis: Doc types › Docteur en Sciences

Contient cette citation

@article{7975da13d034425088040f66dffaa0fb,

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",

note = "Publication code : **RES. ACAD.",

year = "2001",

language = "English",

pages = "399--412",

journal = "Optimization and Engineering",

publisher = "Springer Netherlands",

number = "2",

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T1 - Exploiting band structure in unconstrained optimization without derivatives

AU - Colson, Benoit

AU - Toint, Philippe

N1 - Publication code : **RES. ACAD.

PY - 2001

Y1 - 2001

N2 - 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.

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.

KW - interpolation models

KW - sparsity

KW - trust-region methods

KW - derivative-free optimization

M3 - Article

SP - 399

EP - 412

JO - Optimization and Engineering

JF - Optimization and Engineering

IS - 2

ER -

Exploiting band structure in unconstrained optimization without derivatives

Résumé

Empreinte digitale

Résultat de recherche

BFO, a trainable derivative-free Brute Force Optimizer for nonlinear bound-constrained optimization and equilibrium computations with continuous and discrete variables

Projets

DFO: Algorithmes d'optimisation numérique sans dérivées

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Thèses de l'étudiant

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

Contient cette citation