Recursive trust-region methods for multiscale nonlinear optimization

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Résumé

A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a means of speeding up the computation of the step. This use is recursive, leading to true multilevel/multiscale optimization methods reminiscent of multigrid methods in linear algebra and the solution of partial differential equations. A simple algorithm of the class is then described and its numerical performance is shown to be numerically promising. This observation then motivates a proof of global convergence to first-order stationary points on the fine grid that is valid for all algorithms in the class. © 2008 Society for Industrial and Applied Mathematics.
langue originaleAnglais
Pages (de - à)414-444
Nombre de pages31
journalSIAM Journal on Optimization
Volume19
Numéro de publication1
Les DOIs
étatPublié - 1 janv. 2008

Empreinte digitale

Trust Region Method
Recursive Method
Nonlinear Optimization
Partial differential equations
Linear algebra
Partial differential equation
Multiscale Methods
Nonconvex Optimization
Nonconvex Problems
Multigrid Method
Stationary point
Applied mathematics
Global Convergence
Optimization Methods
Discretization
Valid
Optimization Problem
First-order
Grid
Class

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Recursive trust-region methods for multiscale nonlinear optimization. / Gratton, Serge; Sartenaer, Annick; Toint, Philippe.

Dans: SIAM Journal on Optimization, Vol 19, Numéro 1, 01.01.2008, p. 414-444.

Résultats de recherche: Contribution à un journal/une revueArticle

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