A Homotopy-Based Algorithm for Mixed Complementarity Problems

This paper develops an algorithm for solving mixed complementarity problems which is based upon probability one homotopy methods. After the complementarity problem is reformulated as a system of nonsmooth equations, a homotopy method is used to solve a sequence of smooth approximations to this system of equations. The global convergence properties of this approach are considerably stronger than other recent algorithms, depending on very weak assumptions about the problem. To improve eeciency, the homotopy algorithm is embedded in a generalized Newton-method.