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An accelerated nonmonotone trust region method with adaptive trust region for unconstrained optimization

Author

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  • Jianjun Liu

    (China University of Petroleum)

  • Xiangmin Xu

    (China University of Petroleum)

  • Xuehui Cui

    (China University of Petroleum)

Abstract

Trust region method is a robust method for optimization problems. In this paper, we propose a novel adaptive nonmonotone technique based on trust region methods for solving unconstrained optimization. In order to accelerate the convergence of trust region methods, an adaptive trust region is generated according to the Hessian of the iterate point. Both the nonmonotone techniques and this adaptive strategies can improve the trust region methods in the sense of convergence. We prove that the proposed method is locally superlinear convergence under some standard assumptions. Numerical results show that the new method is effective and has a high speed of convergence in practice.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:69:y:2018:i:1:d:10.1007_s10589-017-9941-6
    DOI: 10.1007/s10589-017-9941-6
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    References listed on IDEAS

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    1. 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.
    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.
    3. Nicholas Gould & Dominique Orban & Philippe Toint, 2015. "CUTEst: a Constrained and Unconstrained Testing Environment with safe threads for mathematical optimization," Computational Optimization and Applications, Springer, vol. 60(3), pages 545-557, April.
    4. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
    5. Shi, Zhenjun & Wang, Shengquan, 2011. "Nonmonotone adaptive trust region method," European Journal of Operational Research, Elsevier, vol. 208(1), pages 28-36, January.
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    Cited by:

    1. M. Ahmadvand & M. Esmaeilbeigi & A. Kamandi & F. M. Yaghoobi, 2019. "A novel hybrid trust region algorithm based on nonmonotone and LOOCV techniques," Computational Optimization and Applications, Springer, vol. 72(2), pages 499-524, March.
    2. Liu, Jianjun & Zhai, Rui & Liu, Yuhan & Li, Wenliang & Wang, Bingzhe & Huang, Liyuan, 2021. "A quasi fractional order gradient descent method with adaptive stepsize and its application in system identification," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    3. Mingming Xu & Quanxin Zhu & Hongying Xiao, 2024. "An Improved Non-Monotonic Adaptive Trust Region Algorithm for Unconstrained Optimization," Mathematics, MDPI, vol. 12(21), pages 1-13, October.

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