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

Hui Huang () and Jiangxing Zhu ()
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Hui Huang: Yunnan University
Jiangxing Zhu: Yunnan University

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 2, No 14, 805-829

Abstract: 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.

Keywords: Quasi-error bound; p-convex set-valued mapping; Inclusion problem; Banach space; 90C25; 90C31; 49J53 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02263-8

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