On gap functions and duality of variational inequality problems

G. Y. Chen, C. J. Goh, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

13 Citations (Scopus)

Abstract

We extend the definition of the gap function defined by Auslender for a more general class of variational inequality problems involving some convex function. A study of the duality of the extended variational inequality problem and its dual sheds new light on the meaning of gap functions. Convexity and differentiability of the gap function are also studied and sufficient conditions are derived. We also show how the gap functions for the primal and the dual are related by dual Fenchel optimization problems.
Original languageEnglish
Pages (from-to)658-673
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume214
Issue number2
DOIs
Publication statusPublished - 15 Oct 1997
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this