IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v67y2017i1d10.1007_s10898-016-0491-8.html
   My bibliography  Save this article

Bounds tightening based on optimality conditions for nonconvex box-constrained optimization

Author

Listed:
  • Yash Puranik

    (Carnegie Mellon University)

  • Nikolaos V. Sahinidis

    (Carnegie Mellon University)

Abstract

First-order optimality conditions have been extensively studied for the development of algorithms for identifying locally optimal solutions. In this work, we propose two novel methods that directly exploit these conditions to expedite the solution of box-constrained global optimization problems. These methods carry out domain reduction by application of bounds tightening methods on optimality conditions. This scheme is implicit and avoids explicit generation of optimality conditions through symbolic differentation, which can be memory and time intensive. The proposed bounds tightening methods are implemented in the global solver BARON. Computational results on a test library of 327 problems demonstrate the value of our proposed approach in reducing the computational time and number of nodes required to solve these problems to global optimality.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-016-0491-8
    DOI: 10.1007/s10898-016-0491-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-016-0491-8
    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/s10898-016-0491-8?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.
    2. Pierre Hansen & Brigitte Jaumard & MichèLe Ruiz & Junjie Xiong, 1993. "Global minimization of indefinite quadratic functions subject to box constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 373-392, April.
    3. Bierlaire, M. & Toint, Ph. L., 1995. "Meuse: An origin-destination matrix estimator that exploits structure," Transportation Research Part B: Methodological, Elsevier, vol. 29(1), pages 47-60, February.
    4. Samuel Burer & Jieqiu Chen, 2011. "Relaxing the optimality conditions of box QP," Computational Optimization and Applications, Springer, vol. 48(3), pages 653-673, April.
    5. Mihály Markót & Hermann Schichl, 2014. "Bound constrained interval global optimization in the COCONUT Environment," Journal of Global Optimization, Springer, vol. 60(4), pages 751-776, December.
    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. 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.
    2. 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.
    3. M. Bierlaire & F. Crittin, 2004. "An Efficient Algorithm for Real-Time Estimation and Prediction of Dynamic OD Tables," Operations Research, INFORMS, vol. 52(1), pages 116-127, February.
    4. Lundgren, Jan T. & Peterson, Anders, 2008. "A heuristic for the bilevel origin-destination-matrix estimation problem," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 339-354, May.
    5. 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.
    6. Hai Yang & Qiang Meng & Michael G. H. Bell, 2001. "Simultaneous Estimation of the Origin-Destination Matrices and Travel-Cost Coefficient for Congested Networks in a Stochastic User Equilibrium," Transportation Science, INFORMS, vol. 35(2), pages 107-123, May.
    7. Michel Bierlaire & Frank Crittin, 2006. "Solving Noisy, Large-Scale Fixed-Point Problems and Systems of Nonlinear Equations," Transportation Science, INFORMS, vol. 40(1), pages 44-63, February.
    8. 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.
    9. Walpen, Jorgelina & Mancinelli, Elina M. & Lotito, Pablo A., 2015. "A heuristic for the OD matrix adjustment problem in a congested transport network," European Journal of Operational Research, Elsevier, vol. 242(3), pages 807-819.
    10. Li, Baibing & Moor, Bart De, 2002. "Dynamic identification of origin-destination matrices in the presence of incomplete observations," Transportation Research Part B: Methodological, Elsevier, vol. 36(1), pages 37-57, January.
    11. Benjamin Beach & Robert Hildebrand & Joey Huchette, 2022. "Compact mixed-integer programming formulations in quadratic optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 869-912, December.
    12. Flurin S. Hänseler & Nicholas A. Molyneaux & Michel Bierlaire, 2017. "Estimation of Pedestrian Origin-Destination Demand in Train Stations," Transportation Science, INFORMS, vol. 51(3), pages 981-997, August.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Bera, Sharminda & Rao, K. V. Krishna, 2011. "Estimation of origin-destination matrix from traffic counts: the state of the art," European Transport \ Trasporti Europei, ISTIEE, Institute for the Study of Transport within the European Economic Integration, issue 49, pages 2-23.
    20. 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.

    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:67:y:2017:i:1:d:10.1007_s10898-016-0491-8. 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.