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A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem

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  • Xiaona Fan

    (School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, P. R. China)

  • Qinglun Yan

    (School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210023, P. R. China)

Abstract

In this paper, we propose a new proof for smoothing homotopy method based on the Fischer–Burmeister function to solve the nonlinear complementarity problem under a nonmonotone solution condition. Under this assumption condition imposed on the defined mapping F, global convergence of a smooth curve determined by the referred homotopy equation is established for almost all initial points in R+n and it is actually regarded as an interior point method. Besides, if the initial point is expanded to Rn, the global convergence of the homotopy method is ensured under a similar condition. The numerical results are reported and illustrate that the method is efficient for some nonlinear complementarity problems.

Suggested Citation

  • Xiaona Fan & Qinglun Yan, 2018. "A New Proof for Global Convergence of a Smoothing Homotopy Method for the Nonlinear Complementarity Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(04), pages 1-13, August.
    • Handle: RePEc:wsi:apjorx:v:35:y:2018:i:04:n:s0217595918500276
    DOI: 10.1142/S0217595918500276
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    References listed on IDEAS

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    1. L. Qi & D. Sun, 2002. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 121-147, April.
    2. Shao-Jian Qu & Mark Goh & Xiujie Zhang, 2011. "A new hybrid method for nonlinear complementarity problems," Computational Optimization and Applications, Springer, vol. 49(3), pages 493-520, July.
    3. 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.
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