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A modulus-based nonmonotone line search method for nonlinear complementarity problems

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  • Zhang, Xu
  • Peng, Zheng

Abstract

A modulus-based nonmonotone line search method is proposed for nonlinear complementarity problem. The considered problem is first reformulated to a nonsmooth nonlinear system based on the modulus-based decomposition. Then a nonmonotone line search method using simulated annealing rule is generalized to solve the resulting system. The global convergence of the proposed method is established under some suitable assumptions. Preliminary numerical experiments show that, compared with some existing methods, the proposed method is feasible and effective.

Suggested Citation

  • Zhang, Xu & Peng, Zheng, 2020. "A modulus-based nonmonotone line search method for nonlinear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    • Handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300320301442
    DOI: 10.1016/j.amc.2020.125175
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    References listed on IDEAS

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    1. Jein-Shan Chen, 2007. "On Some Ncp-Functions Based On The Generalized Fischer–Burmeister Function," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 401-420.
    2. A. Bnouhachem & X. M. Yuan, 2007. "Extended LQP Method for Monotone Nonlinear Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 343-353, December.
    3. Wen, Baolian & Zheng, Hua & Li, Wen & Peng, Xiaofei, 2018. "The relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems of positive definite matrices," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 349-357.
    4. Yuan, Xiao-ming, 2007. "The prediction-correction approach to nonlinear complementarity problems," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1357-1370, February.
    5. Changfeng Ma, 2010. "A new smoothing and regularization Newton method for P 0 -NCP," Journal of Global Optimization, Springer, vol. 48(2), pages 241-261, October.
    6. Wen-Li Dong & Xing Li & Zheng Peng, 2019. "A Simulated Annealing-Based Barzilai–Borwein Gradient Method for Unconstrained Optimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-12, August.
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    Cited by:

    1. Baohua Huang & Wen Li, 2023. "A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 86(1), pages 345-381, September.

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