Characterizations of the solution sets of pseudoinvex programs and variational inequalities

Caiping Liu, Xinmin Yang, Heung Wing Joseph Lee

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

A new concept of nondifferentiable pseudoinvex functions is introduced. Based on the basic properties of this class of pseudoinvex functions, several new and simple characterizations of the solution sets for nondifferentiable pseudoinvex programs are given. Our results are extension and improvement of some results obtained by Mangasarian (Oper. Res. Lett., 7, 21-26, 1988), Jeyakumar and Yang (J. Optim. Theory Appl., 87, 747-755, 1995), Ansari et al. (Riv. Mat. Sci. Econ. Soc., 22, 31-39, 1999), Yang (J. Optim. Theory Appl., 140, 537-542, 2009). The concepts of Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities, defined by upper Dini directional derivative, are introduced. The relationships between the variational-like inequalities and the nondifferentiable pseudoinvex optimization problems are established. And, the characterizations of the solution sets for the Stampacchia-type variational-like inequalities and Minty-type variational-like inequalities are derived.
Original languageEnglish
Article number32
JournalJournal of Inequalities and Applications
Volume2011
DOIs
Publication statusPublished - 1 Dec 2011

Keywords

  • Dini directional derivatives
  • Optimization problem
  • Pseudoinvex programs
  • Solution sets
  • Variational-like inequalities

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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