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

Serge Gratton (serge.gratton***at***cerfacs.fr)
Annick Sartenaer (annick.sartenaer***at***fundp.ac.be)
Philippe Toint (philippe.toint***at***fundp.ac.be)

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.

Keywords: nonlinear optimization, convergence to local minimizers, multilevel problems

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Citation: Report 05/8 Department of Mathematics, University of Namur, Namur, Belgium

Download: [PDF]

Entry Submitted: 02/02/2006
Entry Accepted: 02/02/2006
Entry Last Modified: 02/02/2006

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