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Directional and approximate efficiency in set optimization

Author

Listed:
  • Marius Durea

    (Alexandru Ioan Cuza University
    Iaşi Branch of Romanian Academy)

  • Elena-Andreea Florea

    (Alexandru Ioan Cuza University
    Iaşi Branch of Romanian Academy)

Abstract

We investigate, in the framework of set optimization, some issues that are well studied in vectorial setting, that is, penalization procedures, properness of solutions and optimality conditions on primal spaces. Therefore, with this study we aim at completing the literature dedicated to set optimization with some results that have well established correspondence in the classical vector optimization.

Suggested Citation

  • Marius Durea & Elena-Andreea Florea, 2023. "Directional and approximate efficiency in set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(3), pages 435-459, December.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:3:d:10.1007_s00186-023-00840-1
    DOI: 10.1007/s00186-023-00840-1
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    References listed on IDEAS

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    1. Yu Han & Kai Zhang & Nan-jing Huang, 2020. "The stability and extended well-posedness of the solution sets for set optimization problems via the Painlevé–Kuratowski convergence," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 175-196, February.
    2. Qamrul Hasan Ansari & Andreas H Hamel & Pradeep Kumar Sharma, 2020. "Ekeland’s variational principle with weighted set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 117-136, February.
    3. 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.
    4. Teodor Chelmuş & Marius Durea & Elena-Andreea Florea, 2019. "Directional Pareto Efficiency: Concepts and Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 336-365, July.
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