A new hybrid method for nonlinear complementarity problems

作者：Qu, Shao-Jian^*; Goh, Mark; Zhang, Xiujie

来源：Computational Optimization and Applications, 2011, 49(3): 493-520.

DOI：10.1007/s10589-009-9309-7

• NCP
• Trust region method
• Conic model
• Nonmonotone technique
• Line search

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.

• 出版日期2011-7
• 单位哈尔滨工业大学