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Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems

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  • Y. B. Zhao

    (Chinese Academy of Sciences)

  • J. Y. Han

    (Chinese Academy of Sciences)

Abstract

Two interior-point algorithms using a wide neighborhood of the central path are proposed to solve nonlinear P *-complementarity problems. The proof of the polynomial complexity of the first method requires the problem to satisfy a scaled Lipschitz condition. When specialized to monotone complementarity problems, the results of the first method are similar to those in Ref. 1. The second method is quite different from the first in that the global convergence proof does not require the scaled Lipschitz assumption. However, at each step of this algorithm, one has to compute an approximate solution of a nonlinear system such that a certain accuracy requirement is satisfied.

Suggested Citation

  • Y. B. Zhao & J. Y. Han, 1999. "Two Interior-Point Methods for Nonlinear P *(τ)-Complementarity Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 659-679, September.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:3:d:10.1023_a:1022606324827
    DOI: 10.1023/A:1022606324827
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    References listed on IDEAS

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    1. Shinji Mizuno & Michael J. Todd & Yinyu Ye, 1993. "On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 964-981, November.
    2. McLINDEN, L., 1980. "An analogue of Moreau's proximation theorem, with application to the nonlinear complementarity problem," LIDAM Reprints CORE 443, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
    4. J. H. Wu, 1997. "Modified Primal Path-Following Scheme for the Monotone Variational Inequality Problem," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 189-208, October.
    5. J. Sun & G. Y. Zhao, 1998. "Quadratic Convergence of a Long-Step Interior-Point Method for Nonlinear Monotone Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 471-491, May.
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    Cited by:

    1. G. Wang & C. Yu & K. Teo, 2014. "A full-Newton step feasible interior-point algorithm for $$P_*(\kappa )$$ P ∗ ( κ ) -linear complementarity problems," Journal of Global Optimization, Springer, vol. 59(1), pages 81-99, May.
    2. Huali Zhao & Hongwei Liu, 2018. "A New Infeasible Mehrotra-Type Predictor–Corrector Algorithm for Nonlinear Complementarity Problems Over Symmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 410-427, February.

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