Vector Equilibrium Problems with Generalized Monotone Bifunctions

Monica Bianchi, N. Hadjisavvas, S. Schaible

Research output: Contribution to journalArticle

212 Citations (Scopus)

Abstract

A vector equilibrium problem is defined as follows: given a closed convex subset K of a real topological Hausdorff vector space and a bifunction F(x, y) valued in a real ordered locally convex vector space, find x*∈K such that F(x*, y) ≮0 for all y∈K. This problem generalizes the (scalar) equilibrium problem and the vector variational inequality problem. Extending very recent results for these two special cases, the paper establishes existence of solutions for the unifying model, assuming that F is either a pseudomonotone or quasimonotone bifunction.
Original languageEnglish
Pages (from-to)527-542
Number of pages16
JournalJournal of Optimization Theory and Applications
Volume92
DOIs
Publication statusPublished - 1997

Keywords

  • Pseudomonotone bifunctions
  • Quasimonotone bifunctions
  • Vector equilibrium problems

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