A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems doi:10.3934/jimo.2011.7.977
Zhengyong Zhou - School of Mathematical Sciences, 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.
Received: January 2011; Revised: June 2011; Published: August 2011. |
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