A new hybrid method for nonlinear complementarity problems

  • Authors:

  • Shao-Jian Qu;Mark Goh;Xiujie Zhang

  • Affiliations:

  • Department of Decision Sciences, National University of Singapore, Singapore, Singapore 117592 and Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute Technology, Nangang Dist. ...;Department of Decision Sciences, National University of Singapore, Singapore, Singapore 117592;Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute Technology, Nangang Dist., Harbin, P.R. China 150080

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

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.