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Connectedness of Henig Weakly Efficient Solution Set for Set-Valued Optimization Problems

Author

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  • Q. S. Qiu

    (Zhejiang Normal University)

  • X. M. Yang

    (Chongqing Normal University)

Abstract

In this paper, we study Henig weakly efficient solutions for set-valued optimization problems. The connectedness of the Henig weakly efficient solution set is proved under the condition that the objective function be a cone-arcwise connected set-valued mapping. As an application of the result, we establish the connectedness of the set of super efficient solutions.

Suggested Citation

  • Q. S. Qiu & X. M. Yang, 2012. "Connectedness of Henig Weakly Efficient Solution Set for Set-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 439-449, February.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:2:d:10.1007_s10957-011-9906-3
    DOI: 10.1007/s10957-011-9906-3
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    References listed on IDEAS

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    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. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
    3. Zhong-Fei Li & Shou-Yang Wang, 1998. "Connectedness of super efficient sets in vector optimization of set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 207-217, November.
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    Cited by:

    1. Yu Han & Nan-jing Huang, 2018. "Existence and Connectedness of Solutions for Generalized Vector Quasi-Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 65-85, October.

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