Smooth approximations to nonlinear complementarity problems

It is well known that a nonlinear complementarity problem (NCP) can be formulated as a system of nonsmooth equations. Chen and Mangasarian [Comput. Optim. Appl., 5 (1996), pp. 97-138] proposed a class of parametric smooth functions by twice integrating a probability density function. As a result, the nonsmooth equations can be approximated by smooth equations. This paper refines the smooth functions proposed by Chen and Mangasarian and investigates their structural properties. The refinement allows us to establish the existence, uniqueness, and limiting properties of the trajectory defined by the solutions of these smooth equation approximations. In addition, global error bounds for the NCP with a uniform P-function are obtained.