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Directional derivatives and subdifferentials for set-valued maps applied to set optimization

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Abstract

We present a general method to devise directional derivatives and subdifferentials for set-valued maps that generalize the corresponding constructions from the classical situation of real-valued functions. We show that these generalized differentiation objects enjoy some properties that, on the one hand, meaningfully extend the aforementioned case and, on the another hand, are useful to deal with the so-called \(\ell \)-minimality in set optimization problems.

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Acknowledgements

The authors thank the two anonymous referee for their constructive remarks. This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P4-PCE-2021-0690, within PNCDI III.

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Authors and Affiliations

  1. Faculty of Mathematics, Alexandru Ioan Cuza University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Marius Durea

  2. Octav Mayer Institute of Mathematics of the Romanian Academy, Iaşi, Romania

    Marius Durea

  3. Department of Mathematics, Gh. Asachi Technical University, Bd. Carol I, nr. 11, 700506, Iaşi, Romania

    Radu Strugariu

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  1. Marius Durea
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  2. Radu Strugariu
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Correspondence to Marius Durea.

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Durea, M., Strugariu, R. Directional derivatives and subdifferentials for set-valued maps applied to set optimization. J Glob Optim 85, 687–707 (2023). https://doi.org/10.1007/s10898-022-01222-3

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  • DOI: https://doi.org/10.1007/s10898-022-01222-3

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