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

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

doi:10.1093/imanum/drn034

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 revue › Article

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 originale	Anglais
Pages (de - à)	827-861
Nombre de pages	35
journal	IMA Journal of Numerical Analysis
Volume	28
Numéro de publication	4
Les DOIs	https://doi.org/10.1093/imanum/drn034
état	Publié - 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, S., Mouffe, M., Toint, P., & Weber-Mendona, M. (2008). A recursive ℓ-trust-region method for bound-constrained nonlinear optimization. IMA Journal of Numerical Analysis, 28(4), 827-861. https://doi.org/10.1093/imanum/drn034

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.

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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.",

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Gratton, S, Mouffe, M, Toint, P & Weber-Mendona, M 2008, 'A recursive ℓ-trust-region method for bound-constrained nonlinear optimization', IMA Journal of Numerical Analysis, VOL. 28, Numéro 4, p. 827-861. https://doi.org/10.1093/imanum/drn034

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 revue › Article

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