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On global well-posedness of semi-infinite set optimization problems

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Abstract

This paper aims to study the well-posedness of semi-infinite set optimization problems. We first introduce a notion of global well-posedness for efficient solutions of the reference problems. This notion is then characterized in terms of qualitative properties of approximately minimal solution maps. Next, we extend this notion for perturbed problems obtained by perturbing both the objective set-valued maps and the constraints. Finally, we establish sufficient conditions for the proposed well-posedness by utilizing the Slater constraint qualification and converse properties of the objective set-valued maps.

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Acknowledgements

The authors are very grateful to the editors and anonymous referees for their insightful comments and suggestions that helped us to significantly improve the paper. This research is funded by the University of Science, VNU-HCM, under grant number T2023-06.

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Authors and Affiliations

  1. Department of Mathematics, FPT University, Can Tho, Vietnam

    Tran Quoc Duy

  2. Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam

    Vo Si Trong Long

  3. Vietnam National University, Ho Chi Minh City, Vietnam

    Vo Si Trong Long

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  1. Tran Quoc Duy
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  2. Vo Si Trong Long
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Correspondence to Tran Quoc Duy.

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Duy, T.Q., Long, V.S.T. On global well-posedness of semi-infinite set optimization problems. Comp. Appl. Math. 42, 247 (2023). https://doi.org/10.1007/s40314-023-02383-x

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  • DOI: https://doi.org/10.1007/s40314-023-02383-x

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