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Hartley Proper Efficiency in Multifunction Optimization

Author

Listed:
  • D. S. Kim

    (Pukyong National University)

  • G. M. Lee

    (Pukyong National University)

  • P. H. Sach

    (Hanoi Institute of Mathematics)

Abstract

This paper gives a necessary condition for the Hartley proper efficiency in a vector optimization problem whose objectives and constraints are described by multifunctions F and G. This condition is established under a quasiconvexity requirement of the support functions of F and G or the generalized cone-convexity of a multifunction constructed from F and G.

Suggested Citation

  • D. S. Kim & G. M. Lee & P. H. Sach, 2004. "Hartley Proper Efficiency in Multifunction Optimization," Journal of Optimization Theory and Applications, Springer, vol. 120(1), pages 129-145, January.
    • Handle: RePEc:spr:joptap:v:120:y:2004:i:1:d:10.1023_b:jota.0000012736.02360.58
    DOI: 10.1023/B:JOTA.0000012736.02360.58
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    References listed on IDEAS

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    1. X. M. Yang & X. Q. Yang & G. Y. Chen, 2000. "Theorems of the Alternative and Optimization with Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 627-640, December.
    2. G. Y. Chen & W. D. Rong, 1998. "Characterizations of the Benson Proper Efficiency for Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 365-384, August.
    3. Z. F. Li, 1998. "Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 623-649, September.
    4. 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.
    5. Wen Song, 1998. "A generalization of Fenchel duality in set-valued vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 259-272, November.
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