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

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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.
    Original languageEnglish
    Pages (from-to)676-692
    Number of pages17
    JournalJournal of Computational Mathematics
    Volume24
    Issue number6
    Publication statusPublished - 1 Nov 2006

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