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 parame tric smooth functions by twice integrating a probability density funct ion. As a result, the nonsmooth equations can be approximated by smoot h equations. This paper refines the smooth functions proposed by Chen and Mangasarian and investigates their structural properties. The refi nement 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.