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


  • María Maciel


  • María Mendonça


  • Adriana Verdiell



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

Suggested Citation

  • María Maciel & María Mendonça & Adriana Verdiell, 2013. "Monotone and nonmonotone trust-region-based algorithms for large scale unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 54(1), pages 27-43, January.
  • Handle: RePEc:spr:coopap:v:54:y:2013:i:1:p:27-43 DOI: 10.1007/s10589-012-9477-8

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    References listed on IDEAS

    1. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
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