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On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications

Author

Listed:
  • Nithirat Sisarat

    (Naresuan University)

  • Rabian Wangkeeree

    (Naresuan University
    Naresuan University)

  • Gue Myung Lee

    (Pukyong National University)

Abstract

In this paper, dual characterizations of the containment of two sets involving convex set-valued maps are investigated. These results are expressed in terms of the epigraph of a conjugate function of infima associated with corresponding set-valued maps. As an application, we establish characterizations of weak and proper efficient solutions of set-valued optimization problems in the sense of vector criteria.

Suggested Citation

  • Nithirat Sisarat & Rabian Wangkeeree & Gue Myung Lee, 2020. "On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 824-841, March.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:3:d:10.1007_s10957-019-01605-9
    DOI: 10.1007/s10957-019-01605-9
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    References listed on IDEAS

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    1. Jeyakumar, V. & Lee, G.M. & Dinh, N., 2006. "Characterizations of solution sets of convex vector minimization problems," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1380-1395, November.
    2. Satoshi Suzuki & Daishi Kuroiwa, 2009. "Set containment characterization for quasiconvex programming," Computational Optimization and Applications, Springer, vol. 45(4), pages 551-563, December.
    3. Satoshi Suzuki & Daishi Kuroiwa, 2011. "On Set Containment Characterization and Constraint Qualification for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 554-563, June.
    4. Johannes Jahn & Rüdiger Rauh, 1997. "Contingent epiderivatives and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 193-211, June.
    5. Satoshi Suzuki, 2010. "Set containment characterization with strict and weak quasiconvex inequalities," Journal of Global Optimization, Springer, vol. 47(2), pages 273-285, June.
    6. Nguyen Dinh & Miguel A. Goberna & Dang H. Long & Marco A. López-Cerdá, 2019. "New Farkas-Type Results for Vector-Valued Functions: A Non-abstract Approach," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 4-29, July.
    7. N. Dinh & M. A. Goberna & M. A. López & T. H. Mo, 2017. "Farkas-Type Results for Vector-Valued Functions with Applications," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 357-390, May.
    8. X. Huang & J. Yao, 2013. "Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems," Journal of Global Optimization, Springer, vol. 55(3), pages 611-626, March.
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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.

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