Journal of Industrial and Management Optimization (JIMO)

A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems

Pages: 977 - 989, Volume 7, Issue 4, November 2011      doi:10.3934/jimo.2011.7.977

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Zhengyong Zhou - School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China (email)
Bo Yu - School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China (email)

Abstract: In this paper, a probability-one homotopy method for solving mixed complementarity problems is proposed. The homotopy equation is constructed by using the Robinson's normal equation of mixed complementarity problem and a $C^2$-smooth approximation of projection function. Under the condition that the mixed complementarity problem has no solution at infinity, which is a weaker condition than several well-known ones, existence and convergence of a smooth homotopy path from almost any starting point in $\mathbb{R}^n$ are proven. The homotopy method is implemented in Matlab and numerical results on the MCPLIB test collection are given.

Keywords:  Complementarity problems, smoothing, homotopy method.
Mathematics Subject Classification:  90C33, 65D10, 65H20.

Received: January 2011;      Revised: June 2011;      Available Online: August 2011.