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Characterizations of multi-objective robustness solutions defined by Minkowski set difference

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Listed:
  • Wenyan Han

    (Ningxia University)

  • Guolin Yu

    (North Minzu University)

Abstract

This paper focuses on characterizing the optimality of a kind of partial set order robust solutions, which are defined by Minkowski set difference, for an uncertain multi-objective optimization problem via oriented distance function and image space analysis. Firstly, the relationships between partial set order robust efficiency and upper (lower) set order robust efficiency are illustrated. Secondly, the optimality conditions to partial set order robust solutions are presented by utilizing image space analysis. Furthermore, characterizations are also established for partial set order robust solutions under the assumption of generalized monotonicity, which is determined by an oriented distance function. Finally, an application, namely a shortest path problem, is discussed to verify the effectiveness for the obtained results.

Suggested Citation

  • Wenyan Han & Guolin Yu, 2023. "Characterizations of multi-objective robustness solutions defined by Minkowski set difference," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(4), pages 1361-1380, December.
    • Handle: RePEc:spr:orspec:v:45:y:2023:i:4:d:10.1007_s00291-023-00725-z
    DOI: 10.1007/s00291-023-00725-z
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    References listed on IDEAS

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    1. Johannes Jahn, 2015. "Vectorization in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 783-795, December.
    2. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
    3. Meenakshi Gupta & Manjari Srivastava, 2020. "Approximate Solutions and Levitin–Polyak Well-Posedness for Set Optimization Using Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 191-208, July.
    4. Johannes Jahn & Truong Xuan Duc Ha, 2011. "New Order Relations in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 209-236, February.
    5. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "A Unified Characterization of Multiobjective Robustness via Separation," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 86-102, October.
    6. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 466-493, February.
    7. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    8. Qamrul Hasan Ansari & Elisabeth Köbis & Pradeep Kumar Sharma, 2019. "Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 181(3), pages 817-839, June.
    9. 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.
    10. J. B. Hiriart-Urruty, 1979. "Tangent Cones, Generalized Gradients and Mathematical Programming in Banach Spaces," Mathematics of Operations Research, INFORMS, vol. 4(1), pages 79-97, February.
    11. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.
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