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Nonmonotone derivative-free methods for nonlinear equations

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Abstract

In this paper we study nonmonotone globalization techniques, in connection with iterative derivative-free methods for solving a system of nonlinear equations in several variables. First we define and analyze a class of nonmonotone derivative-free linesearch techniques for unconstrained minimization of differentiable functions. Then we introduce a globalization scheme, which combines nonmonotone watchdog rules and nonmonotone linesearches, and we study the application of this scheme to some recent extensions of the Barzilai–Borwein gradient method and to hybrid stabilization algorithms employing linesearches along coordinate directions. Numerical results on a set of standard test problems show that the proposed techniques can be of value in the solution of large-dimensional systems of equations.

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Buonarroti 12, 00185, Roma, Italy

    L. Grippo

  2. Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185, Roma, Italy

    M. Sciandrone

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  1. L. Grippo
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  2. M. Sciandrone
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Correspondence to M. Sciandrone.

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Grippo, L., Sciandrone, M. Nonmonotone derivative-free methods for nonlinear equations. Comput Optim Appl 37, 297–328 (2007). https://doi.org/10.1007/s10589-007-9028-x

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