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Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P 0 Function

Author

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  • Z.H. Huang

    (Institute of Applied Mathematics)

  • J. Han

    (Institute of Applied Mathematics)

  • Z. Chen

    (Suzhou University)

Abstract

By smoothing a perturbed minimum function, we propose in this paper a new smoothing function. The existence and continuity of a smooth path for solving the nonlinear complementarity problem (NCP) with a P 0 function are discussed. We investigate the boundedness of the iteration sequence generated by noninterior continuation/smoothing methods under the assumption that the solution set of the NCP is nonempty and bounded. Based on the new smoothing function, we present a predictor-corrector smoothing Newton algorithm for solving the NCP with a P 0 function, which is shown to be globally linearly and locally superlinearly convergent under suitable assumptions. Some preliminary computational results are reported.

Suggested Citation

  • Z.H. Huang & J. Han & Z. Chen, 2003. "Predictor-Corrector Smoothing Newton Method, Based on a New Smoothing Function, for Solving the Nonlinear Complementarity Problem with a P 0 Function," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 39-68, April.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:1:d:10.1023_a:1023648305969
    DOI: 10.1023/A:1023648305969
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    References listed on IDEAS

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    1. James V. Burke & Song Xu, 1998. "The Global Linear Convergence of a Noninterior Path-Following Algorithm for Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 719-734, August.
    2. Masakazu Kojima & Nimrod Megiddo & Toshihito Noma, 1991. "Homotopy Continuation Methods for Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 16(4), pages 754-774, November.
    3. M. Seetharama Gowda & Roman Sznajder, 1999. "Weak Univalence and Connectedness of Inverse Images of Continuous Functions," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 255-261, February.
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    Cited by:

    1. Tang, Jingyong & Zhou, Jinchuan & Fang, Liang, 2015. "A non-monotone regularization Newton method for the second-order cone complementarity problem," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 743-756.
    2. 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.
    3. Jingyong Tang & Jinchuan Zhou, 2021. "Quadratic convergence analysis of a nonmonotone Levenberg–Marquardt type method for the weighted nonlinear complementarity problem," Computational Optimization and Applications, Springer, vol. 80(1), pages 213-244, September.
    4. Bilian Chen & Changfeng Ma, 2011. "A new smoothing Broyden-like method for solving nonlinear complementarity problem with a P 0 -function," Journal of Global Optimization, Springer, vol. 51(3), pages 473-495, November.
    5. Liqun Qi & Zheng-Hai Huang, 2019. "Tensor Complementarity Problems—Part II: Solution Methods," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 365-385, November.

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