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Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P 0 -Functions

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  • Yu-Fei Yang
  • Liqun Qi

Abstract

By using the Fischer–Burmeister function to reformulate the nonlinear complementarity problem (NCP) as a system of semismooth equations and using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing trust region algorithm for solving the NCP with P 0 functions. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, local Q-superlinear/Q-quadratic convergence of the algorithm is established without the strict complementarity condition. Copyright Springer Science + Business Media, Inc. 2005

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  • Yu-Fei Yang & Liqun Qi, 2005. "Smoothing Trust Region Methods for Nonlinear Complementarity Problems with P 0 -Functions," Annals of Operations Research, Springer, vol. 133(1), pages 99-117, January.
    • Handle: RePEc:spr:annopr:v:133:y:2005:i:1:p:99-117:10.1007/s10479-004-5026-x
    DOI: 10.1007/s10479-004-5026-x
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    References listed on IDEAS

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    1. Francisco Facchinei, 1998. "Structural and Stability Properties of P 0 Nonlinear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 23(3), pages 735-745, August.
    2. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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    Cited by:

    1. 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.

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