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Characterizations of Multiobjective Robustness via Oriented Distance Function and Image Space Analysis

Author

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  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    King Fahd University of Petroleum and Minerals)

  • Elisabeth Köbis

    (Martin-Luther-University Halle-Wittenberg)

  • Pradeep Kumar Sharma

    (Aligarh Muslim University)

Abstract

In this paper, we characterize different kinds of multiobjective robustness concepts via the well-known oriented distance function. By using characterizations of several set relations via the oriented distance function, together with the help of image space analysis, we construct some suitable subsets of the scalarization image space to obtain equivalent characterizations for various robust solutions for uncertain multiobjective optimization problems based on a set approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:3:d:10.1007_s10957-019-01505-y
    DOI: 10.1007/s10957-019-01505-y
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    Cited by:

    1. 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.
    2. 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.
    3. Khushboo & C. S. Lalitha, 2023. "Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization," Journal of Global Optimization, Springer, vol. 85(1), pages 235-249, January.
    4. S. Khoshkhabar-amiranloo, 2021. "Scalarization of Multiobjective Robust Optimization Problems," SN Operations Research Forum, Springer, vol. 2(3), pages 1-16, September.
    5. 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.
    6. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "Robustness Characterizations for Uncertain Optimization Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 459-479, August.
    7. 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.
    8. Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.
    9. Wang Chen & Xinmin Yang & Yong Zhao, 2023. "Conditional gradient method for vector optimization," Computational Optimization and Applications, Springer, vol. 85(3), pages 857-896, July.

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