IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v84y2022i3d10.1007_s10898-022-01157-9.html
   My bibliography  Save this article

Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints

Author

Listed:
  • Sven de Vries

    (Trier University)

  • Bernd Perscheid

    (Trier University)

Abstract

Cutting planes from the Boolean Quadric Polytope can be used to reduce the optimality gap of the $$\mathcal {NP}$$ NP -hard nonconvex quadratic program with box constraints (BoxQP). It is known that all cuts of the Chvátal–Gomory closure of the Boolean Quadric Polytope are A-odd cycle inequalities. We obtain a compact extended relaxation of all A-odd cycle inequalities, which allows to optimize over the Chvátal–Gomory closure without repeated calls to separation algorithms and has less inequalities than the formulation provided by Boros et al. (SIAM J Discrete Math 5(2):163–177, 1992) for sparse matrices. In a computational study, we confirm the strength of this relaxation and show that we can provide very strong bounds for the BoxQP, even with a plain linear program. The resulting bounds are significantly stronger than these from Bonami et al. (Math Program Comput 10(3):333–382, 2018), which arise from separating A-odd cycle inequalities heuristically.

Suggested Citation

  • Sven de Vries & Bernd Perscheid, 2022. "Tight compact extended relaxations for nonconvex quadratic programming problems with box constraints," Journal of Global Optimization, Springer, vol. 84(3), pages 591-606, November.
    • Handle: RePEc:spr:jglopt:v:84:y:2022:i:3:d:10.1007_s10898-022-01157-9
    DOI: 10.1007/s10898-022-01157-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01157-9
    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/s10898-022-01157-9?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. Samuel Burer & Dieter Vandenbussche, 2009. "Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound," Computational Optimization and Applications, Springer, vol. 43(2), pages 181-195, June.
    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. Jiao, Hongwei & Liu, Sanyang & Lu, Nan, 2015. "A parametric linear relaxation algorithm for globally solving nonconvex quadratic programming," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 973-985.
    2. Hezhi Luo & Yuanyuan Chen & Xianye Zhang & Duan Li & Huixian Wu, 2020. "Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact," Papers 2012.07368, arXiv.org, revised Jan 2021.
    3. Hezhi Luo & Xiaodong Ding & Jiming Peng & Rujun Jiang & Duan Li, 2021. "Complexity Results and Effective Algorithms for Worst-Case Linear Optimization Under Uncertainties," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 180-197, January.
    4. Xiaodong Ding & Hezhi Luo & Huixian Wu & Jianzhen Liu, 2021. "An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation," Computational Optimization and Applications, Springer, vol. 80(1), pages 89-120, September.
    5. X. J. Zheng & X. L. Sun & D. Li, 2010. "Separable Relaxation for Nonconvex Quadratic Integer Programming: Integer Diagonalization Approach," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 463-489, August.
    6. Hanif Sherali & Evrim Dalkiran & Jitamitra Desai, 2012. "Enhancing RLT-based relaxations for polynomial programming problems via a new class of v-semidefinite cuts," Computational Optimization and Applications, Springer, vol. 52(2), pages 483-506, June.
    7. Hezhi Luo & Xianye Zhang & Huixian Wu & Weiqiang Xu, 2023. "Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 199-240, September.
    8. Wei Xia & Juan C. Vera & Luis F. Zuluaga, 2020. "Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 40-56, January.
    9. Christoph Buchheim & Maribel Montenegro & Angelika Wiegele, 2019. "SDP-based branch-and-bound for non-convex quadratic integer optimization," Journal of Global Optimization, Springer, vol. 73(3), pages 485-514, March.
    10. Edirisinghe, Chanaka & Jeong, Jaehwan & Chen, Jingnan, 2021. "Optimal portfolio deleveraging under market impact and margin restrictions," European Journal of Operational Research, Elsevier, vol. 294(2), pages 746-759.
    11. Xiaoli Cen & Yong Xia, 2021. "A New Global Optimization Scheme for Quadratic Programs with Low-Rank Nonconvexity," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1368-1383, October.
    12. Yash Puranik & Nikolaos V. Sahinidis, 2017. "Bounds tightening based on optimality conditions for nonconvex box-constrained optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 59-77, January.
    13. Huixian Wu & Hezhi Luo & Xianye Zhang & Haiqiang Qi, 2023. "An effective global algorithm for worst-case linear optimization under polyhedral uncertainty," Journal of Global Optimization, Springer, vol. 87(1), pages 191-219, September.

    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:84:y:2022:i:3:d:10.1007_s10898-022-01157-9. 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.