# American Institute of Mathematical Sciences

October  2011, 7(4): 977-989. doi: 10.3934/jimo.2011.7.977

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

 1 School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, China 2 School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China

Received  January 2011 Revised  June 2011 Published  August 2011

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.
Citation: Zhengyong Zhou, Bo Yu. A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 977-989. doi: 10.3934/jimo.2011.7.977
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