A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares

Nick Gould, Sven Leyffer, Philippe Toint

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    Abstract

    We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. Preliminary numerical experience is presented that shows substantial gains in efficiency over the traditional monotone trust-region approach. © 2004 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)17-38
    Number of pages22
    JournalSIAM Journal on Optimization
    Volume15
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2005

    Keywords

    • least-squares methods
    • filter methods
    • nonlinear equations
    • Nonlinear optimization
    • convergence theory

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