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

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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 originaleAnglais
Pages (de - à)676-692
Nombre de pages17
journalJournal of Computational Mathematics
Volume24
Numéro de publication6
étatPublié - 1 nov. 2006

Empreinte digitale

Trust Region Method
Convergence Properties
Curvature
Nonconvex Optimization
Optimization
Multigrid Method
Unconstrained Optimization
Minimizer
Objective function
Iteration
Class

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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",
note = "Publication code : FP SB010/2005/08 ; QA 0002.2/001/05/08",
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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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