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

Liqun Qi, Defeng Sun

Research output: Journal article publicationJournal articleAcademic researchpeer-review

57 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)121-147
Number of pages27
JournalJournal of Optimization Theory and Applications
Issue number1
Publication statusPublished - 1 Apr 2002


  • computable smoothing functions
  • quadratic convergence
  • smoothing Newton methods
  • Variational inequality problems

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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