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
état	Publié - 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

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

Colson, Benoit ; Toint, Philippe. / Exploiting band structure in unconstrained optimization without derivatives. Dans: Optimization and Engineering. 2001 ; Numéro 2. p. 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.",

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",

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

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 revue › Article

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T1 - Exploiting band structure in unconstrained optimization without derivatives

AU - Colson, Benoit

AU - Toint, Philippe

N1 - Publication code : **RES. ACAD.

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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

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JO - Optimization and Engineering

JF - Optimization and Engineering

SN - 1389-4420

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