IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v70y2018i4d10.1007_s10898-017-0591-0.html
   My bibliography  Save this article

Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint

Author

Listed:
  • Xiaojin Zheng

    (Tongji University)

  • Yutong Pan

    (Tongji University)

  • Xueting Cui

    (Shanghai University of Finance and Economics)

Abstract

We investigate in this paper nonconvex binary quadratically constrained quadratic programming (QCQP) which arises in various real-life fields. We propose a novel approach of getting quadratic convex reformulation (QCR) for this class of optimization problem. Our approach employs quadratic surrogate functions and convexifies all the quadratic inequality constraints to construct QCR. The price of this approach is the introduction of an extra quadratic inequality. The “best” QCR among the proposed family, in terms that the bound of the corresponding continuous relaxation is best, can be found via solving a semidefinite programming problem. Furthermore, we prove that the bound obtained by continuous relaxation of our best QCR is as tight as Lagrangian bound of binary QCQP. Computational experiment is also conducted to illustrate the solution efficiency improvement of our best QCR when applied in off-the-shell software.

Suggested Citation

  • Xiaojin Zheng & Yutong Pan & Xueting Cui, 2018. "Quadratic convex reformulation for nonconvex binary quadratically constrained quadratic programming via surrogate constraint," Journal of Global Optimization, Springer, vol. 70(4), pages 719-735, April.
    • Handle: RePEc:spr:jglopt:v:70:y:2018:i:4:d:10.1007_s10898-017-0591-0
    DOI: 10.1007/s10898-017-0591-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-017-0591-0
    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/s10898-017-0591-0?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. Klose, Andreas & Drexl, Andreas, 2005. "Facility location models for distribution system design," European Journal of Operational Research, Elsevier, vol. 162(1), pages 4-29, April.
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    4. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    6. X. Cui & X. Zheng & S. Zhu & X. Sun, 2013. "Convex relaxations and MIQCQP reformulations for a class of cardinality-constrained portfolio selection problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1409-1423, August.
    7. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    8. X. Zheng & X. Sun & D. Li, 2011. "Nonconvex quadratically constrained quadratic programming: best D.C. decompositions and their SDP representations," Journal of Global Optimization, Springer, vol. 50(4), pages 695-712, August.
    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. Hezhi Luo & Xiaodi Bai & Jiming Peng, 2019. "Enhancing Semidefinite Relaxation for Quadratically Constrained Quadratic Programming via Penalty Methods," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 964-992, March.
    2. Gonzalez-Feliu, Jesus, 2011. "Freight Distribution Systems with Cross Docking: A Multidisciplinary Analysis," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 51(1).
    3. Yakut, Oguz, 2021. "Implementation of hydraulically driven barrel shooting control by utilizing artificial neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1206-1223.
    4. X. Qin & G. Huang, 2009. "An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(4), pages 661-695, March.
    5. Md. Yousuf Gazi & Khandakar Tahmida Tafhim, 2019. "Investigation of Heavy-mineral Deposits Using Multispectral Satellite Imagery in the Eastern Coastal Margin of Bangladesh," Earth Sciences Malaysia (ESMY), Zibeline International Publishing, vol. 3(2), pages 16-22, October.
    6. Billionnet, Alain, 2011. "Solving the probabilistic reserve selection problem," Ecological Modelling, Elsevier, vol. 222(3), pages 546-554.
    7. Minghe Sun, 2005. "Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 422-437, November.
    8. François Clautiaux & Cláudio Alves & José Valério de Carvalho & Jürgen Rietz, 2011. "New Stabilization Procedures for the Cutting Stock Problem," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 530-545, November.
    9. Kenneth Kletzer & Mr. Barry J. Eichengreen & Mr. Ashoka Mody, 2003. "Crisis Resolution: Next Steps," IMF Working Papers 2003/196, International Monetary Fund.
    10. Tansel, Aysit & Karao?lan, Deniz, 2016. "The Causal Effect of Education on Health Behaviors: Evidence from Turkey," IZA Discussion Papers 10020, Institute of Labor Economics (IZA).
    11. Di Feng & Bettina Klaus, 2022. "Preference revelation games and strict cores of multiple‐type housing market problems," International Journal of Economic Theory, The International Society for Economic Theory, vol. 18(1), pages 61-76, March.
    12. Anna Scherbina, 2021. "Assessing the Optimality of a COVID Lockdown in the United States," Economics of Disasters and Climate Change, Springer, vol. 5(2), pages 177-201, July.
    13. John McKay, 2005. "How Significant and Effective are North Korea's "Market Reforms"?," Global Economic Review, Taylor & Francis Journals, vol. 34(1), pages 83-97.
    14. Timothy K.M. Beatty & Erling Røed Larsen & Dag Einar Sommervoll, 2005. "Measuring the Price of Housing Consumption for Owners in the CPI," Discussion Papers 427, Statistics Norway, Research Department.
    15. Marco Bianchi & Carlos Tapia & Ikerne del Valle, 2020. "Monitoring domestic material consumption at lower territorial levels: A novel data downscaling method," Journal of Industrial Ecology, Yale University, vol. 24(5), pages 1074-1087, October.
    16. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July.
    17. Juarez, Ruben, 2013. "Group strategyproof cost sharing: The role of indifferences," Games and Economic Behavior, Elsevier, vol. 82(C), pages 218-239.
    18. Velloso, Helvia & Vézina, François & Bustillo, Inés, 2006. "The Canadian retirement income system," Documentos de Proyectos 3682, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL).
    19. Melega, Gislaine Mara & de Araujo, Silvio Alexandre & Jans, Raf, 2018. "Classification and literature review of integrated lot-sizing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 271(1), pages 1-19.
    20. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, 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:70:y:2018:i:4:d:10.1007_s10898-017-0591-0. 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.