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Necessary and Sufficient Conditions for Robust Minimal Solutions in Uncertain Vector Optimization

Author

Listed:
  • Marcin Studniarski

    (University of Łódź)

  • Anna Michalak

    (University of Łódź)

  • Aleksandra Stasiak

    (University of Łódź)

Abstract

We introduce a new notion of a vector-based robust minimal solution for a vector-valued uncertain optimization problem, which is defined by means of some open cone. We present necessary and sufficient conditions for this kind of solution, which are stated in terms of some directional derivatives of vector-valued functions. To prove these results, we apply the methods of set-valued analysis. We also study relations between our definition and three other known optimality concepts. Finally, for the case of scalar optimization, we present two general algorithm models for computing vector-based robust minimal solutions.

Suggested Citation

  • Marcin Studniarski & Anna Michalak & Aleksandra Stasiak, 2020. "Necessary and Sufficient Conditions for Robust Minimal Solutions in Uncertain Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 375-397, August.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:2:d:10.1007_s10957-020-01714-w
    DOI: 10.1007/s10957-020-01714-w
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    References listed on IDEAS

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    1. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    2. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    3. Klamroth, Kathrin & Köbis, Elisabeth & Schöbel, Anita & Tammer, Christiane, 2017. "A unified approach to uncertain optimization," European Journal of Operational Research, Elsevier, vol. 260(2), pages 403-420.
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    Cited by:

    1. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.

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