Optimality and error bound for set optimization with application to uncertain multi-objective programming

Wenyan Han and Guolin Yu ()
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Wenyan Han: North Minzu University
Guolin Yu: North Minzu University

Journal of Global Optimization, 2024, vol. 88, issue 4, No 7, 979-998

Abstract: Abstract This paper deals with optimality conditions and error bound for a set optimization problem with the set less order relation. We introduce two kinds of vectorization functions by using the classical oriented distance function, and discuss their properties with respect to the set less order relation. By virtue of the image space analysis, necessary and sufficient optimality conditions for the weak s-minimal solution are established. We propose a regular weak separation function, which is utilized to construct a gap function and an error bound for the set optimization problem. Problems of uncertain multi-objective programming, shortest path and medical image registration are examined as applications of the results established in the paper.

Keywords: Set optimization; Image space analysis; Optimality conditions; Gap function; Error bound (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10898-023-01327-3

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