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Different Conjugate Dual Problems in Vector Optimization and Their Relations

Author

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  • C. R. Chen

    (Chongqing University)

  • S. J. Li

    (Chongqing University)

Abstract

In this paper, three kinds of conjugate dual problems are constructed by virtue of different perturbations to a constrained vector optimization problem. Weak duality, strong duality, and some inclusion relations for the image sets of the three dual problems are established.

Suggested Citation

  • C. R. Chen & S. J. Li, 2009. "Different Conjugate Dual Problems in Vector Optimization and Their Relations," Journal of Optimization Theory and Applications, Springer, vol. 140(3), pages 443-461, March.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:3:d:10.1007_s10957-008-9462-7
    DOI: 10.1007/s10957-008-9462-7
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    References listed on IDEAS

    as
    1. Hidefumi Kawasaki, 1982. "A Duality Theorem in Multiobjective Nonlinear Programming," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 95-110, February.
    2. Hidefumi Kawasaki, 1981. "Conjugate Relations and Weak Subdifferentials of Relations," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 593-607, November.
    3. 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.
    4. R. I. Boţ & G. Kassay & G. Wanka, 2005. "Strong Duality for Generalized Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 127(1), pages 45-70, October.
    Full references (including those not matched with items on IDEAS)

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