Vector Topical Function, Abstract Convexity and Image Space Analysis

Chaoli Yao () and Shengjie Li ()
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Chaoli Yao: Chongqing University
Shengjie Li: Chongqing University

Journal of Optimization Theory and Applications, 2018, vol. 177, issue 3, No 8, 717-742

Abstract: Abstract In this paper, we introduce a new type of vector topical function. It contains some other categories of topical functions as special cases and can be interpreted as weak separation functions in image space analysis. We establish its envelope result and investigate its properties in the frame of abstract convexity. Then, we present the corresponding conjugation and subdifferential, and observe the relationships among these concepts. Finally, as applications, we obtain some dual results for some vector optimization, where the object is expressed as the difference of vector topical functions.

Keywords: Vector topical function; Envelope; Abstract convexity; Vector conjugation; Vector topical optimization; Image space analysis; 90C29; 90C30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1215-7

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