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

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  • Hui Huang

    (Yunnan University)

  • Jiangxing Zhu

    (Yunnan University)

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.

Suggested Citation

  • Hui Huang & Jiangxing Zhu, 2023. "Quasi-Error Bounds for p-Convex Set-Valued Mappings," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 805-829, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02263-8
    DOI: 10.1007/s10957-023-02263-8
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    References listed on IDEAS

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    1. Hoai Le Thi & Tao Pham Dinh & Huynh Ngai, 2012. "Exact penalty and error bounds in DC programming," Journal of Global Optimization, Springer, vol. 52(3), pages 509-535, March.
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    3. Wu Li & Ivan Singer, 1998. "Global Error Bounds for Convex Multifunctions and Applications," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 443-462, May.
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