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Scalarization of Multiobjective Robust Optimization Problems

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  • S. Khoshkhabar-amiranloo

    (Institute for Research in Fundamental Sciences (IPM))

Abstract

In this paper, we introduce several robustness concepts for uncertain multiobjective optimization problems and using polar cone and some scalarization functions we characterize these concepts. We provide some equivalent characterizations for various robust solutions to uncertain multiobjective optimization problems based on a set approach.

Suggested Citation

  • S. Khoshkhabar-amiranloo, 2021. "Scalarization of Multiobjective Robust Optimization Problems," SN Operations Research Forum, Springer, vol. 2(3), pages 1-16, September.
    • Handle: RePEc:spr:snopef:v:2:y:2021:i:3:d:10.1007_s43069-021-00082-z
    DOI: 10.1007/s43069-021-00082-z
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    5. Giovanni P. Crespi & Daishi Kuroiwa & Matteo Rocca, 2017. "Quasiconvexity of set-valued maps assures well-posedness of robust vector optimization," Annals of Operations Research, Springer, vol. 251(1), pages 89-104, April.
    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. 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.
    10. S. Khoshkhabar-amiranloo & E. Khorram, 2015. "Pointwise well-posedness and scalarization in set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 195-210, October.
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