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

Nithirat Sisarat (), Rabian Wangkeeree () and Gue Myung Lee ()
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Nithirat Sisarat: Naresuan University
Rabian Wangkeeree: Naresuan University
Gue Myung Lee: Pukyong National University

Journal of Optimization Theory and Applications, 2020, vol. 184, issue 3, No 6, 824-841

Abstract: 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.

Keywords: Set containment; Convexity of set-valued maps; Set-valued optimization; Optimality conditions; 54C60; 52A41; 49J52; 90C46 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01605-9

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