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A smoothing homotopy method based on Robinson’s normal equation for mixed complementarity problems. (English) Zbl 1231.90360
Summary: 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.

MSC:
 90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) 65D10 Numerical smoothing, curve fitting 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
Matlab
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