IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i1d10.1007_s10957-025-02638-z.html
   My bibliography  Save this article

Qualitative Properties of Robust Benson Efficient Solutions of Uncertain Vector Optimization Problems

Author

Listed:
  • Lam Quoc Anh

    (Can Tho University)

  • Vo Thi Mong Thuy

    (University of Science
    Vietnam National University
    Tay Do University)

  • Xiaopeng Zhao

    (Tiangong University)

Abstract

In this paper, we consider both unconstrained and constrained uncertain vector optimization problems involving free disposal sets, and study the qualitative properties of their robust Benson efficient solutions. First, we discuss necessary and sufficient optimality conditions for the robust Benson efficient solutions of these problems using the linear scalarization method. Then, by utilizing this approach, we investigate the semicontinuity properties of the solution maps when the problem data is perturbed by parameters given in parameter spaces. Finally, we suggest concepts of approximate robust Benson efficient solutions and investigate Hausdorff well-posedness conditions for such problems with respect to these approximate solutions. Several examples are provided to illustrate the applicability and novelty of the results obtained in this study.

Suggested Citation

  • Lam Quoc Anh & Vo Thi Mong Thuy & Xiaopeng Zhao, 2025. "Qualitative Properties of Robust Benson Efficient Solutions of Uncertain Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-37, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02638-z
    DOI: 10.1007/s10957-025-02638-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02638-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-025-02638-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. Chicco & F. Mignanego & L. Pusillo & S. Tijs, 2011. "Vector Optimization Problems via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 516-529, September.
    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. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    4. Erin K. Doolittle & Hervé L. M. Kerivin & Margaret M. Wiecek, 2018. "Robust multiobjective optimization with application to Internet routing," Annals of Operations Research, Springer, vol. 271(2), pages 487-525, December.
    5. Kurt Marti, 2015. "Stochastic Optimization Methods," Springer Books, Springer, edition 3, number 978-3-662-46214-0, December.
    6. R. Tyrrell Rockafellar, 2024. "Distributional robustness, stochastic divergences, and the quadrangle of risk," Computational Management Science, Springer, vol. 21(1), pages 1-30, June.
    7. C. Gutiérrez & B. Jiménez & V. Novo, 2015. "Optimality Conditions for Quasi-Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 796-820, December.
    8. Z. F. Li, 1998. "Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 623-649, September.
    9. Kurt Marti, 2015. "Stochastic Optimization Methods," Springer Books, in: Stochastic Optimization Methods, edition 3, chapter 0, pages 1-35, Springer.
    10. 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.
    11. P. H. Sach, 2003. "Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 335-356, November.
    12. Hui Huang & Haole Zhu, 2022. "Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints," Mathematics, MDPI, vol. 10(23), pages 1-18, December.
    13. Liguo Jiao & Jae Hyoung Lee, 2021. "Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data," Annals of Operations Research, Springer, vol. 296(1), pages 803-820, January.
    14. Zhi-Ang Zhou & Min Kuang, 2023. "Scalarization and Optimality Conditions of E-Globally Proper Efficient Solution for Set-Valued Equilibrium Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 40(02), pages 1-16, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhiang Zhou & Kehui Liang & Qamrul Hasan Ansari, 2025. "Optimality conditions for Benson proper efficiency of set-valued equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(1), pages 111-134, February.
    2. Matteo Rocca, 2025. "Sensitivity to uncertainty and scalarization in robust multiobjective optimization: an overview with application to mean-variance portfolio optimization," Annals of Operations Research, Springer, vol. 346(2), pages 1671-1686, March.
    3. Zhiang Zhou & Wenbin Wei & Fei Huang & Kequan Zhao, 2024. "Approximate weak efficiency of the set-valued optimization problem with variable ordering structures," Journal of Combinatorial Optimization, Springer, vol. 48(3), pages 1-13, October.
    4. P. H. Sach, 2007. "Moreau–Rockafellar Theorems for Nonconvex Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 213-227, May.
    5. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Well-posedness for the optimistic counterpart of uncertain vector optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 517-533, December.
    6. T. D. Chuong & V. H. Mak-Hau & J. Yearwood & R. Dazeley & M.-T. Nguyen & T. Cao, 2022. "Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty," Annals of Operations Research, Springer, vol. 319(2), pages 1533-1564, December.
    7. L. Y. Xia & J. H. Qiu, 2008. "Superefficiency in Vector Optimization with Nearly Subconvexlike Set-Valued Maps," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 125-137, January.
    8. Jian-Wen Peng & Wen-Bin Wei & Refail Kasimbeyli, 2025. "Linear and Nonlinear Scalarization Methods for Vector Optimization Problems with Variable Ordering Structures," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-21, July.
    9. Zhiang Zhou & Wang Chen & Xinmin Yang, 2019. "Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 944-962, December.
    10. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    11. Sarhadi, Hassan & Naoum-Sawaya, Joe & Verma, Manish, 2020. "A robust optimization approach to locating and stockpiling marine oil-spill response facilities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    12. Jeong, Jaehee & Premsankar, Gopika & Ghaddar, Bissan & Tarkoma, Sasu, 2024. "A robust optimization approach for placement of applications in edge computing considering latency uncertainty," Omega, Elsevier, vol. 126(C).
    13. Baker, Erin & Bosetti, Valentina & Salo, Ahti, 2016. "Finding Common Ground when Experts Disagree: Belief Dominance over Portfolios of Alternatives," MITP: Mitigation, Innovation and Transformation Pathways 243147, Fondazione Eni Enrico Mattei (FEEM).
    14. Qiu, Ruozhen & Sun, Minghe & Lim, Yun Fong, 2017. "Optimizing (s, S) policies for multi-period inventory models with demand distribution uncertainty: Robust dynamic programing approaches," European Journal of Operational Research, Elsevier, vol. 261(3), pages 880-892.
    15. Tianyi Han & Liguo Jiao & Jae Hyoung Lee & Junping Yin, 2024. "A utopia point method-based robust vector polynomial optimization scheme," Journal of Global Optimization, Springer, vol. 88(2), pages 461-483, February.
    16. Morteza Davari & Erik Demeulemeester, 2019. "The proactive and reactive resource-constrained project scheduling problem," Journal of Scheduling, Springer, vol. 22(2), pages 211-237, April.
    17. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    18. Jiang, Sheng-Long & Wang, Meihong & Bogle, I. David L., 2023. "Plant-wide byproduct gas distribution under uncertainty in iron and steel industry via quantile forecasting and robust optimization," Applied Energy, Elsevier, vol. 350(C).
    19. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    20. Lamas, Patricio & Goycoolea, Marcos & Pagnoncelli, Bernardo & Newman, Alexandra, 2024. "A target-time-windows technique for project scheduling under uncertainty," European Journal of Operational Research, Elsevier, vol. 314(2), pages 792-806.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02638-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.