Advances and Applications in Statistics
Volume 40, Issue 1, Pages 31 - 60
(May 2014)
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A NEW SMOOTHING NONMONOTONE TRUST REGION METHOD FOR SOLVING NONLINEAR COMPLEMENTARITY PROBLEMS
Ying Ji, Tienan Wang, Yijun Li and Yong Zhou
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Abstract: In this paper, we propose a new smoothing nonmonotone trust region method for solving nonlinear complementarity problems with -functions. First, the nonlinear complementarity problem (NCP) is reformulated as a nonsmooth equation. Then on the basis of the reformulation, a smoothing nonmonotone trust region algorithm via a line search for solving the NCP with functions is proposed. When a trial step is not accepted, the method does not resolve the trust region subproblem but generates an iterative point whose steplength is generated by a formula. 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 the strict complementarity condition. |
Keywords and phrases: NCP, trust region method, fixed steplength, nonmonotone technique. |
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