Abstract
In this paper, a probability-one homotopy method for solvingmixed complementarity problems is proposed. The homotopyequation is constructed by using the Robinson's normal equationof mixed complementarity problem and a $C^2$-smoothapproximation of projection function. Under the condition thatthe 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 almostany starting point in $\mathbb{R}^n$ are proven. The homotopymethod is implemented in Matlab and numerical results on theMCPLIB test collection are given.
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