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Quasi-Error Bounds for p-Convex Set-Valued Mappings

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Abstract

We first introduce the concept of p-convex set-valued mappings, which is an extension of p-convex functions. Then, we show that for a p-convex set optimization problem, a local Pareto minimizer is also a global Pareto minimizer. Moreover, we obtain some results of the type of Robinson–Ursescu theorem for p-convex set-valued mappings in Banach spaces. By adopting a new concept of quasi-error bound for set-valued mappings, we establish some results on the existence of quasi-error bounds for p-convex set-valued mappings.

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Acknowledgements

The authors are indebted to the Associate Editor and the anonymous referees for their helpful remarks, which greatly improved the paper. This work was supported by the National Natural Science Foundation of China (12061085) and the Basic Research Program of Yunnan Province (202001BB050036).

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, People’s Republic of China

    Hui Huang & Jiangxing Zhu

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  1. Hui Huang
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  2. Jiangxing Zhu
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Correspondence to Hui Huang.

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Communicated by Christiane Tammer.

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Huang, H., Zhu, J. Quasi-Error Bounds for p-Convex Set-Valued Mappings. J Optim Theory Appl 198, 805–829 (2023). https://doi.org/10.1007/s10957-023-02263-8

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