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Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 16
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Articles

Abstract convexity of set-valued topical functions with application in DC-type optimization

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Pages 3478-3491 | Received 20 Aug 2019, Accepted 20 Jan 2020, Published online: 03 Feb 2020
 

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.

2010 Mathematics Subject Classifications:

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].

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