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|Title:||A new hybridmethod for nonlinear complementarity problems|
Trust region method
|Citation:||Qu, S.-J., Goh, M., Zhang, X. (2011-07). A new hybridmethod for nonlinear complementarity problems. Computational Optimization and Applications 49 (3) : 493-520. ScholarBank@NUS Repository. https://doi.org/10.1007/s10589-009-9309-7|
|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. © Springer Science+Business Media, LLC 2009.|
|Source Title:||Computational Optimization and Applications|
|Appears in Collections:||Staff Publications|
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