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A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems

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  • M. Reza Peyghami
  • D. Ataee Tarzanagh

Abstract

In this paper, we present a new relaxed nonmonotone trust region method with adaptive radius for solving unconstrained optimization problems. The proposed method combines a relaxed nonmonotone technique with a modified version of the adaptive trust region strategy proposed by Shi and Guo (J Comput Appl Math 213:509–520, 2008 ). Under some suitable and standard assumptions, we establish the global convergence property as well as the superlinear convergence rate for the new method. Numerical results on some test problems show the efficiency and effectiveness of the new proposed method in practice. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • M. Reza Peyghami & D. Ataee Tarzanagh, 2015. "A relaxed nonmonotone adaptive trust region method for solving unconstrained optimization problems," Computational Optimization and Applications, Springer, vol. 61(2), pages 321-341, June.
    • Handle: RePEc:spr:coopap:v:61:y:2015:i:2:p:321-341
    DOI: 10.1007/s10589-015-9726-8
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    References listed on IDEAS

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    1. Y. H. Dai, 2002. "On the Nonmonotone Line Search," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 315-330, February.
    2. Zhaocheng Cui & Boying Wu, 2012. "A new modified nonmonotone adaptive trust region method for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 795-806, December.
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    Cited by:

    1. Jianjun Liu & Xiangmin Xu & Xuehui Cui, 2018. "An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 69(1), pages 77-97, January.
    2. D. Ataee Tarzanagh & M. Reza Peyghami & F. Bastin, 2015. "A New Nonmonotone Adaptive Retrospective Trust Region Method for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 676-692, November.

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