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Existence of Pseudo-Relative Sharp Minimizers in Set-Valued Optimization

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Abstract

In this paper, we propose new concepts of sharp minimality in set-valued optimization problems by means of the pseudo-relative interior, namely pseudo-relative \(\phi \)-sharp minimizers. Based on this notion of minimality, we extend the existence result of a unique minimum of uniformly convex real-valued functions proved by Zălinescu in [25] to vector-valued as well as set-valued maps. Additionally, we provide some existence results for weak sharp minimizers in the sense of Durea and Strugariu [9].

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Acknowledgements

The authors are very grateful to the Editor-in-chief, the Associate Editor as well as the two anonymous referees for their careful reading, valuable remarks and helpful suggestions.

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  1. Faculty of Sciences and Techniques, Cadi Ayyad University, B.P. 549, Marrakech, Morocco

    Tijani Amahroq & Abdessamad Oussarhan

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  1. Tijani Amahroq
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  2. Abdessamad Oussarhan
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Correspondence to Abdessamad Oussarhan.

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Amahroq, T., Oussarhan, A. Existence of Pseudo-Relative Sharp Minimizers in Set-Valued Optimization. Appl Math Optim 84, 2969–2984 (2021). https://doi.org/10.1007/s00245-020-09736-6

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