IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v85y2023i2d10.1007_s10898-022-01209-0.html
   My bibliography  Save this article

Aubin property for solution set in multi-objective programming

Author

Listed:
  • Morteza Rahimi

    (University of Tehran
    Kharazmi University)

  • Majid Soleimani-damaneh

    (University of Tehran)

Abstract

In this paper, the behavior of the solutions of a multi-objective optimization problem, whose the objective functions are perturbed by adding a small linear term, is analyzed. In this regard, a new notion of Lipschitzian stability, by means of the Aubin property of the solution set, is defined. Lipschitz stable locally efficient solutions, as generalization of tilt/full stable solutions, are introduced and characterized by modern variational analysis tools. Applying the weighted sum method, the relationships between these solutions and full-stable local optimal solutions of the scalarized problem are investigated. The key tools in deriving our results come from the first- and second-order variational analysis.

Suggested Citation

  • Morteza Rahimi & Majid Soleimani-damaneh, 2023. "Aubin property for solution set in multi-objective programming," Journal of Global Optimization, Springer, vol. 85(2), pages 441-460, February.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:2:d:10.1007_s10898-022-01209-0
    DOI: 10.1007/s10898-022-01209-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01209-0
    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/s10898-022-01209-0?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. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    2. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, June.
    3. Georgiev, Pando Gr. & Luc, Dinh The & Pardalos, Panos M., 2013. "Robust aspects of solutions in deterministic multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 229(1), pages 29-36.
    4. Sanaz Sadeghi & S. Morteza Mirdehghan, 2018. "Stability of Local Efficiency in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 591-613, August.
    5. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    6. Stephen M. Robinson, 1980. "Strongly Regular Generalized Equations," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 43-62, February.
    7. Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
    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. 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.
    2. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    3. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    4. Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
    5. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    6. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    7. Cecil Ash & Uday Venkatadri & Claver Diallo & Peter Vanberkel & Ahmed Saif, 2023. "PPE Supply Optimization Under Risks of Disruption from the COVID-19 Pandemic," SN Operations Research Forum, Springer, vol. 4(2), pages 1-29, June.
    8. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    9. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    10. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    11. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.
    12. Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    13. M. Durea & R. Strugariu, 2011. "On parametric vector optimization via metric regularity of constraint systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 409-425, December.
    14. Yichen Lu & Chao Yang & Jun Yang, 2022. "A multi-objective humanitarian pickup and delivery vehicle routing problem with drones," Annals of Operations Research, Springer, vol. 319(1), pages 291-353, December.
    15. Bogdana Stanojević & Milan Stanojević & Sorin Nădăban, 2021. "Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    16. Stelios Rozakis & Athanasios Kampas, 2022. "An interactive multi-criteria approach to admit new members in international environmental agreements," Operational Research, Springer, vol. 22(4), pages 3461-3487, September.
    17. Kang, Yan-li & Tian, Jing-Song & Chen, Chen & Zhao, Gui-Yu & Li, Yuan-fu & Wei, Yu, 2021. "Entropy based robust portfolio," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    18. Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.
    19. Min Feng & Shengjie Li & Jie Wang, 2022. "On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 480-503, November.
    20. Fabiana R. Oliveira & Orizon P. Ferreira & Gilson N. Silva, 2019. "Newton’s method with feasible inexact projections for solving constrained generalized equations," Computational Optimization and Applications, Springer, vol. 72(1), pages 159-177, January.

    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:jglopt:v:85:y:2023:i:2:d:10.1007_s10898-022-01209-0. 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.