Smoothing functions and smoothing Newton method for complementarity and variational inequality problems

Authors:
L. Qi;D. Sun
Affiliations:
Professor, Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Assistant Professor, Department of Mathematics, National University of Singapore, Singapore, Republic of Singapore
Venue:
Journal of Optimization Theory and Applications
Year:
2002

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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.