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

Author

Listed:
  • Marius Durea

    (Alexandru Ioan Cuza University
    Octav Mayer Institute of Mathematics of the Romanian Academy)

  • Radu Strugariu

    (Gh. Asachi Technical University)

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 $$\ell $$ ℓ -minimality in set optimization problems.

Suggested Citation

  • Marius Durea & Radu Strugariu, 2023. "Directional derivatives and subdifferentials for set-valued maps applied to set optimization," Journal of Global Optimization, Springer, vol. 85(3), pages 687-707, March.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:3:d:10.1007_s10898-022-01222-3
    DOI: 10.1007/s10898-022-01222-3
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    References listed on IDEAS

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    1. B. Jiménez & V. Novo & A. Vílchez, 2020. "Characterization of set relations through extensions of the oriented distance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 89-115, February.
    2. Kuntal Som & V. Vetrivel, 2021. "On robustness for set-valued optimization problems," Journal of Global Optimization, Springer, vol. 79(4), pages 905-925, April.
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