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A new hybrid method for nonlinear complementarity problems

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Abstract

In this paper, a new hybrid method is proposed for solving nonlinear complementarity problems (NCP) with P 0 function. In the new method, we combine a smoothing nonmonotone trust region method based on a conic model and line search techniques. We reformulate the NCP as a system of semismooth equations using the Fischer-Burmeister function. Using Kanzow’s smooth approximation function to construct the smooth operator, we propose a smoothing nonmonotone trust region algorithm of a conic model for solving the NCP with P 0 functions. This is different from the classical trust region methods, in that when a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength is defined by a line search. We prove that every accumulation point of the sequence generated by the algorithm is a solution of the NCP. Under a nonsingularity condition, the superlinear convergence of the algorithm is established without a strict complementarity condition.

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Authors and Affiliations

  1. Department of Decision Sciences, National University of Singapore, 1 Business Link, Singapore, 117592, Singapore

    Shao-Jian Qu & Mark Goh

  2. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute Technology, Rm. 519, Bldg. 2H, 2 Yikuang Str., Nangang Dist., Harbin, 150080, P.R. China

    Shao-Jian Qu & Xiujie Zhang

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  1. Shao-Jian Qu
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  2. Mark Goh
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  3. Xiujie Zhang
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Correspondence to Shao-Jian Qu.

Additional information

This work was supported by the National Science Foundation Grant of China. This work was supported by both China Post-doctoral Science Foundation (No. 01107172) and Heilongjiang Province Post-doctoral Science Foundation (No. 01106961).

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Qu, SJ., Goh, M. & Zhang, X. A new hybrid method for nonlinear complementarity problems. Comput Optim Appl 49, 493–520 (2011). https://doi.org/10.1007/s10589-009-9309-7

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  • DOI: https://doi.org/10.1007/s10589-009-9309-7

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