Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization

Serge Gratton; Annick Sartenaer; Philippe Toint

Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization

Serge Gratton, Annick Sartenaer, Philippe Toint

Departement de Mathematique

Résultats de recherche: Contribution à un journal/une revue › Article

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Résumé

Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of test directions and may not be available at every iteration. It is shown that convergence to local weak minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.

langue originale	Anglais
Pages (de - à)	676-692
Nombre de pages	17
journal	Journal of Computational Mathematics
Volume	24
Numéro de publication	6
état	Publié - 1 nov. 2006

Empreinte digitale

Trust Region Method

Convergence Properties

Curvature

Nonconvex Optimization

Optimization

Multigrid Method

Unconstrained Optimization

Minimizer

Objective function

Iteration

Class

Citer ceci

Gratton, S., Sartenaer, A., & Toint, P. (2006). Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Journal of Computational Mathematics, 24(6), 676-692.

Gratton, Serge ; Sartenaer, Annick ; Toint, Philippe. / Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Dans: Journal of Computational Mathematics. 2006 ; Vol 24, Numéro 6. p. 676-692.

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abstract = "Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of test directions and may not be available at every iteration. It is shown that convergence to local weak minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.",

author = "Serge Gratton and Annick Sartenaer and Philippe Toint",

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Gratton, S, Sartenaer, A & Toint, P 2006, 'Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization', Journal of Computational Mathematics, VOL. 24, Numéro 6, p. 676-692.

Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. / Gratton, Serge; Sartenaer, Annick ; Toint, Philippe.

Dans: Journal of Computational Mathematics, Vol 24, Numéro 6, 01.11.2006, p. 676-692.

Résultats de recherche: Contribution à un journal/une revue › Article

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N2 - Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of test directions and may not be available at every iteration. It is shown that convergence to local weak minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.

AB - Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of test directions and may not be available at every iteration. It is shown that convergence to local weak minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.

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Gratton S, Sartenaer A , Toint P. Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization. Journal of Computational Mathematics. 2006 nov. 1;24(6):676-692.