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A smoothing Newton method based on the modulus equation for a class of weakly nonlinear complementarity problems

Author

Listed:
  • Baohua Huang

    (Fujian Normal University)

  • Wen Li

    (South China Normal University)

Abstract

By equivalently transforming a class of weakly nonlinear complementarity problems into a modulus equation, and introducing a smoothing approximation of the absolute value function, a smoothing Newton method is established for solving the weakly nonlinear complementarity problem. Under some mild assumptions, the proposed method is shown to possess global convergence and locally quadratical convergence. Especially, the global convergence results do not need a priori existence of an accumulation point with some suitable conditions. Numerical results are given to show the efficiency of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00482-3
    DOI: 10.1007/s10589-023-00482-3
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    References listed on IDEAS

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    1. Zhang, Xu & Peng, Zheng, 2020. "A modulus-based nonmonotone line search method for nonlinear complementarity problems," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    2. Zheng, Hua & Vong, Seakweng & Liu, Ling, 2019. "A direct preconditioned modulus-based iteration method for solving nonlinear complementarity problems of H-matrices," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 396-405.
    3. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    4. Xia, Zechen & Li, Chenliang, 2015. "Modulus-based matrix splitting iteration methods for a class of nonlinear complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 34-42.
    5. Stephen M. Robinson, 1992. "Normal Maps Induced by Linear Transformations," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 691-714, August.
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