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On Essential Stable Sets of Solutions in Set Optimization Problems

Author

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  • Q. Q. Song

    (Guilin University of Technology)

  • G. Q. Tang

    (Guilin University of Technology)

  • L. S. Wang

    (China Agricultural University)

Abstract

This paper introduces the essential stability for set optimization problems. Some kinds of essential stable sets of weakly minimal and minimal solutions are shown. The graph of minimal solution mappings is not necessarily closed, which is different from weakly minimal solution mappings. The existence of minimum essential sets of minimal solutions is proved.

Suggested Citation

  • Q. Q. Song & G. Q. Tang & L. S. Wang, 2013. "On Essential Stable Sets of Solutions in Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 591-599, March.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:3:d:10.1007_s10957-012-0129-z
    DOI: 10.1007/s10957-012-0129-z
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    References listed on IDEAS

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    1. Ruchi, Arora & Lalitha, C.S., 2005. "Proximal proper efficiency in set-valued optimization," Omega, Elsevier, vol. 33(5), pages 407-411, October.
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    3. Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
    4. M. Chinaie & J. Zafarani, 2009. "Image Space Analysis and Scalarization of Multivalued Optimization," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 451-467, September.
    5. P. Q. Khanh & N. H. Quan, 2011. "Generic Stability and Essential Components of Generalized KKM Points and Applications," Journal of Optimization Theory and Applications, Springer, vol. 148(3), pages 488-504, March.
    6. P. Khanh & D. Quy, 2011. "On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings," Journal of Global Optimization, Springer, vol. 49(3), pages 381-396, March.
    7. Q. Luo, 1999. "Essential Component and Essential Optimum Solution of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 433-438, August.
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    Cited by:

    1. Shiva Kapoor & C. S. Lalitha, 2021. "Essential stability in unified vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 161-175, May.

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