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Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems

  • María Maciel

    ()

  • María Mendonça

    ()

  • Adriana Verdiell

    ()

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    Two trust regions algorithms for unconstrained nonlinear optimization problems are presented: a monotone and a nonmonotone one. Both of them solve the trust region subproblem by the spectral projected gradient (SPG) method proposed by Birgin, Martínez and Raydan (in SIAM J. Optim. 10(4):1196–1211, 2000 ). SPG is a nonmonotone projected gradient algorithm for solving large-scale convex-constrained optimization problems. It combines the classical projected gradient method with the spectral gradient choice of steplength and a nonmonotone line search strategy. The simplicity (only requires matrix-vector products, and one projection per iteration) and rapid convergence of this scheme fits nicely with globalization techniques based on the trust region philosophy, for large-scale problems. In the nonmonotone algorithm the trial step is evaluated by acceptance via a rule which can be considered a generalization of the well known fraction of Cauchy decrease condition and a generalization of the nonmonotone line search proposed by Grippo, Lampariello and Lucidi (in SIAM J. Numer. Anal. 23:707–716, 1986 ). Convergence properties and extensive numerical results are presented. Our results establish the robustness and efficiency of the new algorithms. Copyright Springer Science+Business Media, LLC 2013

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    File URL: http://hdl.handle.net/10.1007/s10589-012-9477-8
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    Article provided by Springer in its journal Computational Optimization and Applications.

    Volume (Year): 54 (2013)
    Issue (Month): 1 (January)
    Pages: 27-43

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    Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:27-43
    Contact details of provider: Web page: http://www.springer.com/math/journal/10589

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