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

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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.

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Acknowledgements

The authors are extremely thankful to the anonymous referees and the editor for providing several suggestions to improve the paper to its current form greatly. This research was supported by the Thailand Research Fund through the Royal Golden Jubilee Ph.D. Program (Grant No. PHD/0026/2555), the Thailand Research Fund, Grant No. RSA6080077, and Naresuan University. The third author was supported by the National Research Foundation of Korea (NRF) Grant funded by Korea government (MSIT) (NRF-2017R1E1A1A03069931).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Nithirat Sisarat & Rabian Wangkeeree

  2. Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, Thailand

    Rabian Wangkeeree

  3. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Korea

    Gue Myung Lee

Authors
  1. Nithirat Sisarat
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  2. Rabian Wangkeeree
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  3. Gue Myung Lee
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Correspondence to Rabian Wangkeeree.

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Regina S. Burachik.

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Sisarat, N., Wangkeeree, R. & Lee, G.M. On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications. J Optim Theory Appl 184, 824–841 (2020). https://doi.org/10.1007/s10957-019-01605-9

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  • DOI: https://doi.org/10.1007/s10957-019-01605-9

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