On the gap functions of prevariational inequalities

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Abstract

Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian.
Original languageEnglish
Pages (from-to)437-452
Number of pages16
JournalJournal of Optimization Theory and Applications
Volume116
Issue number2
DOIs
Publication statusPublished - 1 Feb 2003

Keywords

  • gap functions
  • Lagrangian functions
  • linear fractional functions
  • Variational inequalities

ASJC Scopus subject areas

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

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