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