A neural network based on the generalized Fischer-Burmeister function for nonlinear complementarity problems

Authors:
Jein-Shan Chen;Chun-Hsu Ko;Shaohua Pan
Affiliations:
Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan;Department of Electrical Engineering, I-Shou University, Kaohsiung 840, Taiwan;School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China
Venue:
Information Sciences: an International Journal
Year:
2010

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Abstract

In this paper, we consider a neural network model for solving the nonlinear complementarity problem (NCP). The neural network is derived from an equivalent unconstrained minimization reformulation of the NCP, which is based on the generalized Fischer-Burmeister function @f"p(a,b)=@?(a,b)@?"p-(a+b). We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability as well as exponential stability. It was found that a larger p leads to a better convergence rate of the trajectory. Numerical simulations verify the obtained theoretical results.