IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v77y2020i4d10.1007_s10898-020-00905-z.html
   My bibliography  Save this article

An enhanced logical benders approach for linear programs with complementarity constraints

Author

Listed:
  • Francisco Jara-Moroni

    (Universidad de Santiago de Chile)

  • John E. Mitchell

    (Rensselaer Polytechnic Institute)

  • Jong-Shi Pang

    (University of Southern California)

  • Andreas Wächter

    (Northwestern University)

Abstract

This work extends the logical benders approach for solving linear programs with complementarity constraints proposed by Hu et al. (SIAM J Optim 19(1):445–471, 2008) and Bai et al. (Comput Optim Appl 54(3):517–554, 2013). We develop a novel interpretation of the logical Benders method as a reversed branch-and-bound search, where the whole exploration procedure starts from the leaf nodes in an enumeration tree. This insight enables us to provide a new framework over which we can combine master problem and cut generation in a single process. It also allows us to diversify the search, leading computationally to stronger cuts. We also present an optimization-based sparsification process which makes the cut generation more efficient. Numerical results are presented to show the effectiveness of this enhanced method. Results are also extended to problems with more complementarity constraints, exceeding those that can be handled by the original method in the cited references.

Suggested Citation

  • Francisco Jara-Moroni & John E. Mitchell & Jong-Shi Pang & Andreas Wächter, 2020. "An enhanced logical benders approach for linear programs with complementarity constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 687-714, August.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:4:d:10.1007_s10898-020-00905-z
    DOI: 10.1007/s10898-020-00905-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00905-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/s10898-020-00905-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. Toshihide Ibaraki, 1973. "Technical Note—The Use of Cuts in Complementary Programming," Operations Research, INFORMS, vol. 21(1), pages 353-359, February.
    2. Jing Hu & John Mitchell & Jong-Shi Pang & Bin Yu, 2012. "On linear programs with linear complementarity constraints," Journal of Global Optimization, Springer, vol. 53(1), pages 29-51, May.
    3. Pietro Belotti & Pierre Bonami & Matteo Fischetti & Andrea Lodi & Michele Monaci & Amaya Nogales-Gómez & Domenico Salvagnin, 2016. "On handling indicator constraints in mixed integer programming," Computational Optimization and Applications, Springer, vol. 65(3), pages 545-566, December.
    4. Matteo Fischetti & Michele Monaci, 2014. "Exploiting Erraticism in Search," Operations Research, INFORMS, vol. 62(1), pages 114-122, February.
    5. Toshihide Ibaraki, 1971. "Technical Note—Complementary Programming," Operations Research, INFORMS, vol. 19(6), pages 1523-1529, October.
    6. Alejandro Marcos Alvarez & Quentin Louveaux & Louis Wehenkel, 2017. "A Machine Learning-Based Approximation of Strong Branching," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 185-195, February.
    7. Andrea Lodi & Giulia Zarpellon, 2017. "Rejoinder on: On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 247-248, July.
    8. Andrea Lodi & Giulia Zarpellon, 2017. "On learning and branching: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 207-236, July.
    9. Lijie Bai & John Mitchell & Jong-Shi Pang, 2013. "On convex quadratic programs with linear complementarity constraints," Computational Optimization and Applications, Springer, vol. 54(3), pages 517-554, April.
    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. Jacquet, Quentin & van Ackooij, Wim & Alasseur, Clémence & Gaubert, Stéphane, 2024. "Quadratic regularization of bilevel pricing problems and application to electricity retail markets," European Journal of Operational Research, Elsevier, vol. 313(3), pages 841-857.

    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. Bissan Ghaddar & Ignacio Gómez-Casares & Julio González-Díaz & Brais González-Rodríguez & Beatriz Pateiro-López & Sofía Rodríguez-Ballesteros, 2023. "Learning for Spatial Branching: An Algorithm Selection Approach," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1024-1043, September.
    2. Dimitris Bertsimas & Cheol Woo Kim, 2023. "A Prescriptive Machine Learning Approach to Mixed-Integer Convex Optimization," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1225-1241, November.
    3. Yu Yang & Natashia Boland & Martin Savelsbergh, 2021. "Multivariable Branching: A 0-1 Knapsack Problem Case Study," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1354-1367, October.
    4. Nikolaus Furian & Michael O’Sullivan & Cameron Walker & Eranda Çela, 2021. "A machine learning-based branch and price algorithm for a sampled vehicle routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 693-732, September.
    5. Bengio, Yoshua & Lodi, Andrea & Prouvost, Antoine, 2021. "Machine learning for combinatorial optimization: A methodological tour d’horizon," European Journal of Operational Research, Elsevier, vol. 290(2), pages 405-421.
    6. Dimitris Bertsimas & Bartolomeo Stellato, 2022. "Online Mixed-Integer Optimization in Milliseconds," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2229-2248, July.
    7. Álinson S. Xavier & Feng Qiu & Shabbir Ahmed, 2021. "Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 739-756, May.
    8. Yang, Yu & Boland, Natashia & Dilkina, Bistra & Savelsbergh, Martin, 2022. "Learning generalized strong branching for set covering, set packing, and 0–1 knapsack problems," European Journal of Operational Research, Elsevier, vol. 301(3), pages 828-840.
    9. Brais González-Rodríguez & Joaquín Ossorio-Castillo & Julio González-Díaz & Ángel M. González-Rueda & David R. Penas & Diego Rodríguez-Martínez, 2023. "Computational advances in polynomial optimization: RAPOSa, a freely available global solver," Journal of Global Optimization, Springer, vol. 85(3), pages 541-568, March.
    10. Shen, Yunzhuang & Sun, Yuan & Li, Xiaodong & Eberhard, Andrew & Ernst, Andreas, 2023. "Adaptive solution prediction for combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1392-1408.
    11. Emilio Carrizosa & Dolores Romero Morales, 2024. "Guest editorial to the Special Issue on Machine Learning and Mathematical Optimization in TOP-Transactions in Operations Research," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 351-353, October.
    12. Alberto Pia & Jeff Linderoth & Haoran Zhu, 2024. "Relaxations and cutting planes for linear programs with complementarity constraints," Journal of Global Optimization, Springer, vol. 90(1), pages 27-51, September.
    13. Gambella, Claudio & Ghaddar, Bissan & Naoum-Sawaya, Joe, 2021. "Optimization problems for machine learning: A survey," European Journal of Operational Research, Elsevier, vol. 290(3), pages 807-828.
    14. Eric Larsen & Sébastien Lachapelle & Yoshua Bengio & Emma Frejinger & Simon Lacoste-Julien & Andrea Lodi, 2022. "Predicting Tactical Solutions to Operational Planning Problems Under Imperfect Information," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 227-242, January.
    15. Juho Lauri & Sourav Dutta & Marco Grassia & Deepak Ajwani, 2023. "Learning fine-grained search space pruning and heuristics for combinatorial optimization," Journal of Heuristics, Springer, vol. 29(2), pages 313-347, June.
    16. Ahmet Herekoğlu & Özgür Kabak, 2024. "Crew recovery optimization with deep learning and column generation for sustainable airline operation management," Annals of Operations Research, Springer, vol. 342(1), pages 399-427, November.
    17. Charly Robinson La Rocca & Jean-François Cordeau & Emma Frejinger, 2024. "One-Shot Learning for MIPs with SOS1 Constraints," SN Operations Research Forum, Springer, vol. 5(3), pages 1-28, September.
    18. Christoph Hertrich & Martin Skutella, 2023. "Provably Good Solutions to the Knapsack Problem via Neural Networks of Bounded Size," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1079-1097, September.
    19. Emilio Carrizosa & Cristina Molero-Río & Dolores Romero Morales, 2021. "Mathematical optimization in classification and regression trees," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 5-33, April.
    20. Renke Kuhlmann, 2019. "Learning to steer nonlinear interior-point methods," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(4), pages 381-419, December.

    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:77:y:2020:i:4:d:10.1007_s10898-020-00905-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.