IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v250y2015icp973-985.html
   My bibliography  Save this article

A parametric linear relaxation algorithm for globally solving nonconvex quadratic programming

Author

Listed:
  • Jiao, Hongwei
  • Liu, Sanyang
  • Lu, Nan

Abstract

In this article, we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming (NQP). In this algorithm, a new parametric linearized technique is proposed for generating parametric linear relaxation programming (PLRP) of the NQP, which can be used to determine the lower bound of global minimum value of the NQP. To improve the convergent speed of the proposed algorithm, a pruning operation is employed to compress the investigated region. By subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain, the proposed algorithm is convergent to the global minimum of the NQP. Finally, an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:973-985
    DOI: 10.1016/j.amc.2014.11.032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314015550
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.11.032?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. N. V. Thoai, 2000. "Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints," Journal of Optimization Theory and Applications, Springer, vol. 107(2), pages 331-354, November.
    3. Minyue Fu & Zhi-Quan Luo & Yinyu Ye, 1998. "Approximation Algorithms for Quadratic Programming," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 29-50, March.
    4. Lin, Ming-Hua & Tsai, Jung-Fa, 2012. "Range reduction techniques for improving computational efficiency in global optimization of signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 216(1), pages 17-25.
    5. Peiping Shen & Xiaoai Li, 2013. "Branch-reduction-bound algorithm for generalized geometric programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1123-1142, July.
    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. Chenyang Hu & Yuelin Gao & Fuping Tian & Suxia Ma, 2022. "A Relaxed and Bound Algorithm Based on Auxiliary Variables for Quadratically Constrained Quadratic Programming Problem," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2023. "Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems," Journal of Global Optimization, Springer, vol. 86(1), pages 61-92, May.

    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. Tseng, Chung-Li & Zhan, Yiduo & Zheng, Qipeng P. & Kumar, Manish, 2015. "A MILP formulation for generalized geometric programming using piecewise-linear approximations," European Journal of Operational Research, Elsevier, vol. 245(2), pages 360-370.
    2. 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.
    3. Shen, Peiping & Zhu, Zeyi & Chen, Xiao, 2019. "A practicable contraction approach for the sum of the generalized polynomial ratios problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 36-48.
    4. Sturm, J.F. & Zhang, S., 2001. "On Cones of Nonnegative Quadratic Functions," Discussion Paper 2001-26, Tilburg University, Center for Economic Research.
    5. 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.
    6. Zhuoyi Xu & Linbin Li & Yong Xia, 2023. "A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 93-109, August.
    7. Alexandre Belloni & Robert M. Freund & Santosh Vempala, 2009. "An Efficient Rescaled Perceptron Algorithm for Conic Systems," Mathematics of Operations Research, INFORMS, vol. 34(3), pages 621-641, August.
    8. Lu, Hao-Chun, 2020. "Indicator of power convex and exponential transformations for solving nonlinear problems containing posynomial terms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    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. Peiping Shen & Kaimin Wang & Ting Lu, 2020. "Outer space branch and bound algorithm for solving linear multiplicative programming problems," Journal of Global Optimization, Springer, vol. 78(3), pages 453-482, November.
    11. D. Henrion & S. Tarbouriech & D. Arzelier, 2001. "LMI Approximations for the Radius of the Intersection of Ellipsoids: Survey," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 1-28, January.
    12. Tongli Zhang & Yong Xia, 2022. "Comment on “Approximation algorithms for quadratic programming”," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1099-1103, September.
    13. Armin Jabbarzadeh & Leyla Aliabadi & Reza Yazdanparast, 2021. "Optimal payment time and replenishment decisions for retailer’s inventory system under trade credit and carbon emission constraints," Operational Research, Springer, vol. 21(1), pages 589-620, March.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Duy-Van Nguyen, 2022. "Strong Duality for General Quadratic Programs with Quadratic Equality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 297-313, October.
    19. Wasim Akram Mandal, 2021. "Weighted Tchebycheff Optimization Technique Under Uncertainty," Annals of Data Science, Springer, vol. 8(4), pages 709-731, December.
    20. 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.

    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:apmaco:v:250:y:2015:i:c:p:973-985. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.