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

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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.

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Acknowledgements

This research was supported by Natural Science Foundation of China under Grant No. 12361062 and Natural Science Foundation of Ningxia Provincial of China under Grant No. 2023AAC02053.

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  1. School of Mathematics and Information Science, North Minzu University, Yinchuan, 750021, China

    Wenyan Han & Guolin Yu

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  1. Wenyan Han
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  2. Guolin Yu
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Correspondence to Guolin Yu.

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Han, W., Yu, G. Optimality and error bound for set optimization with application to uncertain multi-objective programming. J Glob Optim 88, 979–998 (2024). https://doi.org/10.1007/s10898-023-01327-3

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