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A non-monotone regularization Newton method for the second-order cone complementarity problem

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  • Tang, Jingyong
  • Zhou, Jinchuan
  • Fang, Liang

Abstract

Based on the smoothing Newton method and the Tikhonov regularization method, we construct a regularization Newton method for the second-order cone complementarity problem. The method uses a non-monotone line search scheme which contains the usual monotone line search as a special case. By using the theory of Euclidean Jordan algebras, we prove that the proposed method is globally and locally quadratically convergent under suitable assumptions. Some numerical results are reported which indicate the effectiveness of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:743-756
    DOI: 10.1016/j.amc.2015.09.017
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    References listed on IDEAS

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    1. Zheng-Hai Huang & Tie Ni, 2010. "Smoothing algorithms for complementarity problems over symmetric cones," Computational Optimization and Applications, Springer, vol. 45(3), pages 557-579, April.
    2. 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.
    3. Yasushi Narushima & Nobuko Sagara & Hideho Ogasawara, 2011. "A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 149(1), pages 79-101, April.
    4. 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.
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