Continuation method for nonlinear complementarity problems via normal maps

In a recent paper by Chen and Mangasarian a class of parametric smoothing functions has been proposed to approximate the plus function present in many optimization and complementarity related problems. This paper uses these smoothing functions to approximate the normal map formulation of nonlinear complementarity problems (NCPs). Properties of the smoothing function are investigated based on the density functions that define the smooth approximations. A continuation method is then proposed to solve the NCPs arising from the approximations. Sufficient conditions are provided to guarantee the boundedness of the solution trajectory. Furthermore, the structure of the subproblem arising in the proposed continuation method is analyzed for different choices of smoothing functions. Computational results of the continuation method are reported.