The global linear convergence of an infeasible non-interior path-following algorithm for complementarity problems with uniform P-functions

We propose an infeasible non-interior path-following method for nonlinear complementarity problems with uniform P-functions. This method is based on the smoothing techniques introduced by Kanzow. A key to our analysis is the introduction of a new notion of neighborbood for the central path which is suitable for infeasible non-interior path-following methods. By restricting the iterates in the neighborhood of the central path, we provide a systematic procedure to update the smoothing parameter and establish the global linear convergence of this method. Some preliminary computational results are reported.