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ABSTRACT
In the previous work, we established a conjugate duality for the constrained vector optimization, in which the concept of a set-valued topical function introduced there played a key role. This is a map with good features and can be interpreted as an abstract convex function in some sense. This paper is devoted to the further study for the properties and characterizations of the set-valued topical function, within the framework of abstract convexity, especially about the subdifferentials. As applications, we also investigate some set-valued DC-type optimization problems. Some optimal conditions and dual results are obtained by virtue of the conjugation and subdifferentials.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
This research was partially supported by the National Natural Science Foundation of China [Grant numbers: 11971393,11401487,11601437], the Fundamental Research Funds for the Central Universities [Grant numbers: XDJK2020B048], the Science and Technology Research Program of Chongqing Municipal Education Commission [Grant numbers: KJ1713334], Natural Science Foundation of Chongqing, China [Grant numbers: cstc2019jcyj-bshX0107] and Chongqing Research Program of Basic Research and Frontier Technology [Grant numbers: cstc2016jcyjA0239 and cstc2016jcyjA0141].