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

Author

Listed:
  • P. H. Sach

    (Institute of Mathematics)

  • D. S. Kim

    (Pukyong National University)

  • L. A. Tuan

    (Ninh Thuan College of Pedagogy)

  • G. M. Lee

    (Pukyong National University)

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.

Suggested Citation

  • P. H. Sach & D. S. Kim & L. A. Tuan & G. M. Lee, 2008. "Duality Results for Generalized Vector Variational Inequalities with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 105-123, January.
    • Handle: RePEc:spr:joptap:v:136:y:2008:i:1:d:10.1007_s10957-007-9342-6
    DOI: 10.1007/s10957-007-9342-6
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    References listed on IDEAS

    as
    1. X. M. Yang & D. Li & S. Y. Wang, 2001. "Near-Subconvexlikeness in Vector Optimization with Set-Valued Functions," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 413-427, August.
    2. P. H. Sach, 2003. "Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 335-356, November.
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