Recursive trust-region methods for multiscale nonlinear optimization

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    Abstract

    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.
    Original languageEnglish
    Pages (from-to)414-444
    Number of pages31
    JournalSIAM Journal on Optimization
    Volume19
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2008

    Keywords

    • nonlinear optimization
    • recursive algorithms
    • simplified models
    • multilevel problems
    • convergence theory

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