IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v131y2006i2d10.1007_s10957-006-9136-2.html
   My bibliography  Save this article

Multicriteria Approach to Bilevel Optimization

Author

Listed:
  • J. Fliege

    (University of Birmingham)

  • L. N. Vicente

    (Universidade de Coimbra)

Abstract

In this paper, we study the relationship between bilevel optimization and multicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower-level problem of the bilevel optimization problem is convex and continuously differentiable in the lower-level variables, this order relation is equivalent to a second, more tractable order relation. Then, we show how to construct a (nonconvex) cone for which we can prove that the nondominated points with respect to the order relation induced by the cone are also nondominated points with respect to any of the two order relations mentioned before. We comment also on the practical and computational implications of our approach.

Suggested Citation

  • J. Fliege & L. N. Vicente, 2006. "Multicriteria Approach to Bilevel Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 209-225, November.
    • Handle: RePEc:spr:joptap:v:131:y:2006:i:2:d:10.1007_s10957-006-9136-2
    DOI: 10.1007/s10957-006-9136-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9136-2
    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/s10957-006-9136-2?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. A. Haurie & G. Savard & D. J. White, 1990. "A Note on: An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem," Operations Research, INFORMS, vol. 38(3), pages 553-555, June.
    2. Jörg Fliege, 2004. "Gap-free computation of Pareto-points by quadratic scalarizations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 69-89, February.
    3. Marcotte, Patrice, 1988. "A note on a bilevel programming algorithm by Leblanc and Boyce," Transportation Research Part B: Methodological, Elsevier, vol. 22(3), pages 233-236, June.
    4. P. A. Clark & A. W. Westerberg, 1988. "A note on the optimality conditions for the bilevel programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(5), pages 413-418, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sauli Ruuska & Kaisa Miettinen & Margaret M. Wiecek, 2012. "Connections Between Single-Level and Bilevel Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 60-74, April.
    2. Rihab Said & Maha Elarbi & Slim Bechikh & Lamjed Ben Said, 2022. "Solving combinatorial bi-level optimization problems using multiple populations and migration schemes," Operational Research, Springer, vol. 22(3), pages 1697-1735, July.
    3. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    4. A. Georgantas, 2020. "Robust Optimization Approaches for Portfolio Selection: A Computational and Comparative Analysis," Papers 2010.13397, arXiv.org.
    5. Chi-Bin Cheng & Hsu-Shih Shih & Boris Chen, 2017. "Subsidy rate decisions for the printer recycling industry by bi-level optimization techniques," Operational Research, Springer, vol. 17(3), pages 901-919, October.
    6. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    7. J. Glackin & J. G. Ecker & M. Kupferschmid, 2009. "Solving Bilevel Linear Programs Using Multiple Objective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 197-212, February.
    8. Shahabeddin Najafi & Masoud Hajarian, 2023. "Multiobjective Conjugate Gradient Methods on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1229-1248, June.

    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. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    2. G. Cocchi & M. Lapucci, 2020. "An augmented Lagrangian algorithm for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 29-56, September.
    3. Jörg Fliege, 2006. "An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 825-845, November.
    4. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.
    5. H. I. Calvete & C. Galé, 1998. "On the Quasiconcave Bilevel Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 98(3), pages 613-622, September.
    6. Clegg, J. & Smith, M. J., 2001. "Cone projection versus half-space projection for the bilevel optimisation of transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 35(1), pages 71-82, January.
    7. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    8. Liu, Yi-Hsin & Spencer, Thomas H., 1995. "Solving a bilevel linear program when the inner decision maker controls few variables," European Journal of Operational Research, Elsevier, vol. 81(3), pages 644-651, March.
    9. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    10. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.

    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:131:y:2006:i:2:d:10.1007_s10957-006-9136-2. 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.