On the Existence of Super Efficient Solutions and Optimality Conditions for Set-Valued Vector Optimization Problems

Lu-Chuan Ceng, Ching-Feng Wen and Yeong-Cheng Liou
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Lu-Chuan Ceng: Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
Ching-Feng Wen: Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
Yeong-Cheng Liou: Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan

Mathematics, 2022, vol. 10, issue 3, 1-14

Abstract: In this paper, by using the normal subdifferential and equilibrium-like function we first obtain some properties for K -preinvex set-valued maps. Secondly, in terms of this equilibrium-like function, we establish some sufficient conditions for the existence of super minimal points of a K -preinvex set-valued map, that is, super efficient solutions of a set-valued vector optimization problem, and also attain necessity optimality terms for a general type of super efficiency.

Keywords: K -preinvex multi-valued map; normal subdifferential; equilibrium-like function; set-valued vector optimization problem; super efficient solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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