Generalized convex functions and vector variational inequalities

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Abstract

In this paper, (α, φ, Q)-invexity is introduced, where α:X ×X → int Rm+, φ:X ×X →X, X is a Banach space, Q is a convex cone of Rm. This unifies the properties of many classes of functions, such as Q-convexity, pseudo-linearity, representation condition, null space condition, and V-invexity. A generalized vector variational inequality is considered, and its equivalence with a multi-objective programming problem is discussed using (α, φ, Q)-invexity. An existence theorem for the solution of a generalized vector variational inequality is proved. Some applications of (α, φ, Q)-invexity to multi-objective programming problems and to a special kind of generalized vector variational inequality are given.
Original languageEnglish
Pages (from-to)563-580
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume79
Issue number3
DOIs
Publication statusPublished - 1 Dec 1993
Externally publishedYes

Keywords

  • Generalized convex functions
  • generalized vector variational inequalities
  • multi-objective programming problems
  • necessary and sufficient conditions

ASJC Scopus subject areas

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

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