A new hybrid method for nonlinear complementarity problems |
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Authors: | Shao-Jian Qu Mark Goh Xiujie Zhang |
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Institution: | 1.Department of Decision Sciences,National University of Singapore,Singapore,Singapore;2.Academy of Fundamental and Interdisciplinary Sciences,Harbin Institute Technology,Nangang Dist., Harbin,P.R. China |
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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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Keywords: | |
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