Solving the nonlinear complementarity problem via an aggregate homotopy method

Authors:
Xiaona Fan;Qinglun Yan;Junxiang Li
Affiliations:
College of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210046, China.;College of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210046, China.;School of Economics and Management, Tongji University, Shanghai 200092, China
Venue:
International Journal of Computer Applications in Technology
Year:
2012

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Abstract

In this paper, by using the idea of the aggregate function method, a new aggregate homotopy method is proposed to solve the nonlinear complementarity problem (NCP). The homotopy equation is constructed based on the aggregate function which is the smooth approximation to the reformulation of the NCP. An existence condition for a finite homotopy path is derived from the limiting behaviours of the complementarity mapping at infinity. This condition is different from any existing ones in the literature but can be easily verified. The results provide a theoretical basis to develop a new computational method for NCP. The numerical experiment results show the method is effective.