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Journal of Optimization Theory and Applications

, Volume 136, Issue 1, pp 105–123 | Cite as

Duality Results for Generalized Vector Variational Inequalities with Set-Valued Maps

  • P. H. Sach
  • D. S. Kim
  • L. A. Tuan
  • G. M. LeeEmail author
Article

Abstract

In this paper, we introduce new dual problems of generalized vector variational inequality problems with set-valued maps and we discuss a link between the solution sets of the primal and dual problems. The notion of solutions in each of these problems is introduced via the concepts of efficiency, weak efficiency or Benson proper efficiency in vector optimization. We provide also examples showing that some earlier duality results for vector variational inequality may not be true.

Keywords

Vector variational inequalities Set-valued maps Duality Conjugate maps Biconjugate maps 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • P. H. Sach
    • 1
  • D. S. Kim
    • 2
  • L. A. Tuan
    • 3
  • G. M. Lee
    • 2
    Email author
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Department of Applied MathematicsPukyong National UniversityPusanRepublic of Korea
  3. 3.Ninh Thuan College of PedagogyNinh ThuanVietnam

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