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Optimality Conditions in Uncertain Vector Optimization Problems with Variable Domination Structures via Gerstewitz Function

Author

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  • Zhenzhen Qin

    (Chongqing Jiaotong University)

  • Qilin Wang

    (Chongqing Jiaotong University)

  • Jie Wang

    (Chongqing Jiaotong University)

  • Ching-Feng Wen

    (National Yunlin University of Science and Technology)

Abstract

In this paper, we first investigate a few important properties of several set-order relations via the Gerstewitz function. Secondly, employing several set-order relations, we examine a unified approach to characterize robust strictly minimal solutions for uncertain vector optimization problems with variable domination structures. Finally, by utilizing scalarization methods, we establish the necessary and sufficient conditions for the robust strictly minimal solution of uncertain vector optimization problems with variable domination structures under more generalized assumptions.

Suggested Citation

  • Zhenzhen Qin & Qilin Wang & Jie Wang & Ching-Feng Wen, 2025. "Optimality Conditions in Uncertain Vector Optimization Problems with Variable Domination Structures via Gerstewitz Function," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-23, November.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:2:d:10.1007_s10957-025-02783-5
    DOI: 10.1007/s10957-025-02783-5
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    References listed on IDEAS

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    1. Chen Chen & Yu Wei, 2019. "Robust multiobjective portfolio optimization: a set order relations approach," Journal of Combinatorial Optimization, Springer, vol. 38(1), pages 21-49, July.
    2. Elisa Caprari & Lorenzo Cerboni Baiardi & Elena Molho, 2022. "Scalarization and robustness in uncertain vector optimization problems: a non componentwise approach," Journal of Global Optimization, Springer, vol. 84(2), pages 295-320, October.
    3. Truong Q. Bao & Boris S. Mordukhovich & Antoine Soubeyran & Christiane Tammer, 2022. "Vector Optimization with Domination Structures: Variational Principles and Applications," Post-Print hal-03528619, HAL.
    4. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part I: Set Relations and Relationship to Vector Approach," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 931-946, December.
    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    6. Jiawei Chen & La Huang & Shengjie Li, 2018. "Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 794-823, September.
    7. Gabriele Eichfelder & Maria Pilecka, 2016. "Set Approach for Set Optimization with Variable Ordering Structures Part II: Scalarization Approaches," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 947-963, December.
    8. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    9. Bokrantz, Rasmus & Fredriksson, Albin, 2017. "Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 262(2), pages 682-692.
    10. 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.
    11. 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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