Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems

Abstract

This paper provides for the first time some computable smoothing functions for variational inequality problems with general constraints. This paper proposes also a new version of the smoothing Newton method and establishes its global and superlinear (quadratic) convergence under conditions weaker than those previously used in the literature. These are achieved by introducing a general definition for smoothing functions, which include almost all the existing smoothing functions as special cases.