A recursive ℓ-trust-region method for bound-constrained nonlinear optimization

Serge Gratton, M. Mouffe, Philippe Toint, M. Weber-Mendona

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.
langue originaleAnglais
Pages (de - à)827-861
Nombre de pages35
journalIMA Journal of Numerical Analysis
Volume28
Numéro de publication4
Les DOIs
étatPublié - 1 oct. 2008

Empreinte digitale

Trust Region Method
Recursive Method
Constrained Optimization
Nonlinear Optimization
Trust Region
Smoothing Techniques
Nonconvex Optimization
Nonconvex Problems
Critical point
Theoretical Analysis
Discretization
Infinity
Optimization Problem
First-order
Norm
Hierarchy

Citer ceci

Gratton, Serge ; Mouffe, M. ; Toint, Philippe ; Weber-Mendona, M. / A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. Dans: IMA Journal of Numerical Analysis. 2008 ; Vol 28, Numéro 4. p. 827-861.
@article{8a734926383043b1b53c399452f59305,
title = "A recursive ℓ-trust-region method for bound-constrained nonlinear optimization",
abstract = "A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.",
author = "Serge Gratton and M. Mouffe and Philippe Toint and M. Weber-Mendona",
note = "Copyright 2008 Elsevier B.V., All rights reserved.",
year = "2008",
month = "10",
day = "1",
doi = "10.1093/imanum/drn034",
language = "English",
volume = "28",
pages = "827--861",
journal = "IMA Journal of Numerical Analysis",
issn = "0272-4979",
publisher = "Oxford University Press",
number = "4",

}

A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. / Gratton, Serge; Mouffe, M.; Toint, Philippe; Weber-Mendona, M.

Dans: IMA Journal of Numerical Analysis, Vol 28, Numéro 4, 01.10.2008, p. 827-861.

Résultats de recherche: Contribution à un journal/une revueArticle

TY - JOUR

T1 - A recursive ℓ-trust-region method for bound-constrained nonlinear optimization

AU - Gratton, Serge

AU - Mouffe, M.

AU - Toint, Philippe

AU - Weber-Mendona, M.

N1 - Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2008/10/1

Y1 - 2008/10/1

N2 - A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.

AB - A recursive trust-region method is introduced for the solution of bound-cons-trained nonlinear nonconvex optimization problems for which a hierarchy of descriptions exists. Typical cases are infinite-dimensional problems for which the levels of the hierarchy correspond to discretization levels, from coarse to fine. The new method uses the infinity norm to define the shape of the trust region, which is well adapted to the handling of bounds and also to the use of successive coordinate minimization as a smoothing technique. Numerical tests motivate a theoretical analysis showing convergence to first-order critical points irrespective of the starting point.

UR - http://www.scopus.com/inward/record.url?scp=55849087653&partnerID=8YFLogxK

U2 - 10.1093/imanum/drn034

DO - 10.1093/imanum/drn034

M3 - Article

AN - SCOPUS:55849087653

VL - 28

SP - 827

EP - 861

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

IS - 4

ER -