A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

Serge Gratton, Mélodie Mouffe, Philippe Toint, Melissa Weber Mendonca

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. Some numerical tests are presented to motivate a theoretical analysis showing convergence to first-order critical points irrespective of the given starting point.
langue originaleAnglais
Pages (de - à)827-861
Nombre de pages35
journalIMA Journal of Numerical Analysis
Volume28
Numéro de publication4
étatNon publié - 2008

Empreinte digitale

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

Citer ceci

Gratton, Serge ; Mouffe, Mélodie ; Toint, Philippe ; Weber Mendonca, Melissa. / A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization. Dans: IMA Journal of Numerical Analysis. 2008 ; Vol 28, Numéro 4. p. 827-861.
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A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization. / Gratton, Serge; Mouffe, Mélodie; Toint, Philippe; Weber Mendonca, Melissa.

Dans: IMA Journal of Numerical Analysis, Vol 28, Numéro 4, 2008, p. 827-861.

Résultats de recherche: Contribution à un journal/une revueArticle

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T1 - A recursive trust-region method in infinity norm for bound-constrained nonlinear optimization

AU - Gratton, Serge

AU - Mouffe, Mélodie

AU - Toint, Philippe

AU - Weber Mendonca, Melissa

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PY - 2008

Y1 - 2008

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. Some numerical tests are presented to motivate a theoretical analysis showing convergence to first-order critical points irrespective of the given starting point.

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KW - nonlinear optimization

KW - Recursive methods

KW - convergence theory

KW - multilevel problems

M3 - Article

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SP - 827

EP - 861

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

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