IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v197y2009i1p36-41.html
   My bibliography  Save this article

An exact penalty on bilevel programs with linear vector optimization lower level

Author

Listed:
  • Ankhili, Z.
  • Mansouri, A.

Abstract

We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples.

Suggested Citation

  • Ankhili, Z. & Mansouri, A., 2009. "An exact penalty on bilevel programs with linear vector optimization lower level," European Journal of Operational Research, Elsevier, vol. 197(1), pages 36-41, August.
  • Handle: RePEc:eee:ejores:v:197:y:2009:i:1:p:36-41
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00480-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gal, Tomas, 1977. "A general method for determining the set of all efficient solutions to a linear vectormaximum problem," European Journal of Operational Research, Elsevier, vol. 1(5), pages 307-322, September.
    2. James E. Falk & Karla R. Hoffman, 1976. "A Successive Underestimation Method for Concave Minimization Problems," Mathematics of Operations Research, INFORMS, vol. 1(3), pages 251-259, August.
    3. Philip B. Zwart, 1974. "Global Maximization of a Convex Function with Linear Inequality Constraints," Operations Research, INFORMS, vol. 22(3), pages 602-609, June.
    4. Campelo, Manoel & Scheimberg, Susana, 2000. "A note on a modified simplex approach for solving bilevel linear programming problems," European Journal of Operational Research, Elsevier, vol. 126(2), pages 454-458, October.
    5. H. Bonnel & J. Morgan, 2006. "Semivectorial Bilevel Optimization Problem: Penalty Approach," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 365-382, December.
    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. Kahina Ghazli & Nicolas Gillis & Mustapha Moulaï, 2020. "Optimizing over the properly efficient set of convex multi-objective optimization problems," Annals of Operations Research, Springer, vol. 295(2), pages 575-604, December.
    2. Yunjia Ma & Wei Xu & Lianjie Qin & Xiujuan Zhao, 2019. "Site Selection Models in Natural Disaster Shelters: A Review," Sustainability, MDPI, vol. 11(2), pages 1-24, January.
    3. Calvete, Herminia I. & Galé, Carmen, 2011. "On linear bilevel problems with multiple objectives at the lower level," Omega, Elsevier, vol. 39(1), pages 33-40, January.
    4. Alves, Maria João & Henggeler Antunes, Carlos, 2022. "A new exact method for linear bilevel problems with multiple objective functions at the lower level," European Journal of Operational Research, Elsevier, vol. 303(1), pages 312-327.
    5. Zhiqing Meng & Chuangyin Dang & Rui Shen & Ming Jiang, 2012. "An Objective Penalty Function of Bilevel Programming," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 377-387, May.
    6. Henri Bonnel & Julien Collonge, 2014. "Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 405-427, August.
    7. Henri Bonnel & Léonard Todjihoundé & Constantin Udrişte, 2015. "Semivectorial Bilevel Optimization on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 464-486, November.
    8. Maria João Alves & Carlos Henggeler Antunes & João Paulo Costa, 2021. "New concepts and an algorithm for multiobjective bilevel programming: optimistic, pessimistic and moderate solutions," Operational Research, Springer, vol. 21(4), pages 2593-2626, December.
    9. Henri Bonnel & Christopher Schneider, 2019. "Post-Pareto Analysis and a New Algorithm for the Optimal Parameter Tuning of the Elastic Net," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 993-1027, December.

    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. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2023. "A general purpose exact solution method for mixed integer concave minimization problems," European Journal of Operational Research, Elsevier, vol. 309(3), pages 977-992.
    2. Queiroz, Marcelo & Humes, Carlos, 2003. "A heuristic for the continuous capacity and flow assignment," European Journal of Operational Research, Elsevier, vol. 146(3), pages 444-459, May.
    3. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    4. Sinha, Ankur & Das, Arka & Anand, Guneshwar & Jayaswal, Sachin, 2021. "A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems (revised as on 12/08/2021)," IIMA Working Papers WP 2021-03-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. A.P. Wierzbicki, 1998. "Reference Point Methods in Vector Optimization and Decision Support," Working Papers ir98017, International Institute for Applied Systems Analysis.
    6. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    7. Sylva, John & Crema, Alejandro, 2007. "A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1011-1027, August.
    8. S. Razavyan, 2016. "A Method for Generating a Well-Distributed Pareto Set in Multiple Objective Mixed Integer Linear Programs Based on the Decision Maker’s Initial Aspiration Level," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-23, August.
    9. Harold P. Benson & S. Selcuk Erenguc, 1990. "An algorithm for concave integer minimization over a polyhedron," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 515-525, August.
    10. Arevalo Quijada, Mª Teresa & Zapata Reina, Asunción, 1996. "La programación fraccionada múltiple: tratamiento del problema de la producción," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 6, pages 5-24, Diciembre.
    11. Harold P. Benson, 2006. "Maximizing the ratio of two convex functions over a convex set," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(4), pages 309-317, June.
    12. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    13. Strijbosch, L.W.G. & van Doorne, A.G.M. & Selen, W.J., 1990. "A simplified MOLP algorithm : The MOLP-S procedure," Research Memorandum FEW 460, Tilburg University, School of Economics and Management.
    14. Dempe, S., 2011. "Comment to "interactive fuzzy goal programming approach for bilevel programming problem" by S.R. Arora and R. Gupta," European Journal of Operational Research, Elsevier, vol. 212(2), pages 429-431, July.
    15. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
    16. Aharon Ben-Tal & Ernst Roos, 2022. "An Algorithm for Maximizing a Convex Function Based on Its Minimum," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3200-3214, November.
    17. H. P. Benson, 1998. "Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 17-35, July.
    18. Harold P. Benson, 1996. "Deterministic algorithms for constrained concave minimization: A unified critical survey," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(6), pages 765-795, September.
    19. Wei Chen & Milind Dawande & Ganesh Janakiraman, 2014. "Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory Application," Operations Research, INFORMS, vol. 62(1), pages 81-103, February.
    20. Calvete, Herminia I. & Galé, Carmen, 2011. "On linear bilevel problems with multiple objectives at the lower level," Omega, Elsevier, vol. 39(1), pages 33-40, 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:eee:ejores:v:197:y:2009:i:1:p:36-41. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.