IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v86y2023i1d10.1007_s10898-022-01255-8.html
   My bibliography  Save this article

Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems

Author

Listed:
  • Bo Zhang

    (Ningxia University
    Ningxia University)

  • YueLin Gao

    (North Minzu University
    North Minzu University)

  • Xia Liu

    (Ningxia University)

  • XiaoLi Huang

    (North Minzu University)

Abstract

The quadratically constrained quadratic programming problem often appears in various fields such as engineering practice, management science and network communication. This paper mainly considers a non-convex quadratic programming problem with convex quadratic constraints. Firstly, the objective function of the problem is reconstructed into a form composed of only one convex function and several linear functions by using the eigenvalue decomposition technique of matrix. Then the reconstructed problem is converted to the equivalent problem with simple concave quadratic objective function in the outcome space by introducing appropriate auxiliary variables, and its feasible domain is convex. Based on the branch-and-bound framework which can guarantee the global optimality of the solution, a global optimization algorithm for solving the equivalent problem is proposed, which integrates the effective relaxation process and the branching process related to the outer approximation technique. Finally, the effectiveness and feasibility of the algorithm are illustrated by numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:86:y:2023:i:1:d:10.1007_s10898-022-01255-8
    DOI: 10.1007/s10898-022-01255-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-022-01255-8
    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/s10898-022-01255-8?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. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    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. Deng, Zhibin & Fang, Shu-Cherng & Jin, Qingwei & Xing, Wenxun, 2013. "Detecting copositivity of a symmetric matrix by an adaptive ellipsoid-based approximation scheme," European Journal of Operational Research, Elsevier, vol. 229(1), pages 21-28.
    4. Bomze, Immanuel M., 2012. "Copositive optimization – Recent developments and applications," European Journal of Operational Research, Elsevier, vol. 216(3), pages 509-520.
    5. 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.
    6. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
    7. Cheng Lu & Zhibin Deng & Qingwei Jin, 2017. "An eigenvalue decomposition based branch-and-bound algorithm for nonconvex quadratic programming problems with convex quadratic constraints," Journal of Global Optimization, Springer, vol. 67(3), pages 475-493, March.
    8. Godai Azuma & Mituhiro Fukuda & Sunyoung Kim & Makoto Yamashita, 2022. "Exact SDP relaxations of quadratically constrained quadratic programs with forest structures," Journal of Global Optimization, Springer, vol. 82(2), pages 243-262, February.
    9. Ashtiani, Alireza M. & Ferreira, Paulo A.V., 2015. "A branch-and-cut algorithm for a class of sum-of-ratios problems," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 596-608.
    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. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2022. "An Outcome-Space-Based Branch-and-Bound Algorithm for a Class of Sum-of-Fractions Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(3), pages 830-855, March.
    2. Cheng Lu & Zhibin Deng & Qingwei Jin, 2017. "An eigenvalue decomposition based branch-and-bound algorithm for nonconvex quadratic programming problems with convex quadratic constraints," Journal of Global Optimization, Springer, vol. 67(3), pages 475-493, March.
    3. Deng, Zhibin & Fang, Shu-Cherng & Jin, Qingwei & Xing, Wenxun, 2013. "Detecting copositivity of a symmetric matrix by an adaptive ellipsoid-based approximation scheme," European Journal of Operational Research, Elsevier, vol. 229(1), pages 21-28.
    4. Bomze, Immanuel M. & Gabl, Markus, 2023. "Optimization under uncertainty and risk: Quadratic and copositive approaches," European Journal of Operational Research, Elsevier, vol. 310(2), pages 449-476.
    5. Immanuel Bomze & Werner Schachinger & Gabriele Uchida, 2012. "Think co(mpletely)positive ! Matrix properties, examples and a clustered bibliography on copositive optimization," Journal of Global Optimization, Springer, vol. 52(3), pages 423-445, March.
    6. Akihiro Tanaka & Akiko Yoshise, 2018. "LP-based tractable subcones of the semidefinite plus nonnegative cone," Annals of Operations Research, Springer, vol. 265(1), pages 155-182, June.
    7. Cheng Lu & Zhibin Deng & Jing Zhou & Xiaoling Guo, 2019. "A sensitive-eigenvector based global algorithm for quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 73(2), pages 371-388, February.
    8. Li, Xiaobo & Natarajan, Karthik & Teo, Chung-Piaw & Zheng, Zhichao, 2014. "Distributionally robust mixed integer linear programs: Persistency models with applications," European Journal of Operational Research, Elsevier, vol. 233(3), pages 459-473.
    9. Immanuel Bomze & Markus Gabl, 2021. "Interplay of non-convex quadratically constrained problems with adjustable robust optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(1), pages 115-151, February.
    10. Shota Takahashi & Mituhiro Fukuda & Mirai Tanaka, 2022. "New Bregman proximal type algorithms for solving DC optimization problems," Computational Optimization and Applications, Springer, vol. 83(3), pages 893-931, December.
    11. Xiangyu Cui & Xun Li & Duan Li & Yun Shi, 2014. "Time Consistent Behavior Portfolio Policy for Dynamic Mean-Variance Formulation," Papers 1408.6070, arXiv.org, revised Aug 2015.
    12. Shinji Yamada & Akiko Takeda, 2018. "Successive Lagrangian relaxation algorithm for nonconvex quadratic optimization," Journal of Global Optimization, Springer, vol. 71(2), pages 313-339, June.
    13. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2015. "On a Smooth Dual Gap Function for a Class of Player Convex Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 659-685, August.
    14. João Carlos O. Souza & Paulo Roberto Oliveira & Antoine Soubeyran, 2016. "Global convergence of a proximal linearized algorithm for difference of convex functions," Post-Print hal-01440298, HAL.
    15. Boglárka G.-Tóth & Kristóf Kovács, 2016. "Solving a Huff-like Stackelberg location problem on networks," Journal of Global Optimization, Springer, vol. 64(2), pages 233-247, February.
    16. Aras Selvi & Aharon Ben-Tal & Ruud Brekelmans & Dick den Hertog, 2022. "Convex Maximization via Adjustable Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2091-2105, July.
    17. Andrey Afonin & Roland Hildebrand & Peter J. C. Dickinson, 2021. "The extreme rays of the $$6\times 6$$ 6 × 6 copositive cone," Journal of Global Optimization, Springer, vol. 79(1), pages 153-190, January.
    18. Ben-Tal, A. & den Hertog, D., 2011. "Immunizing Conic Quadratic Optimization Problems Against Implementation Errors," Discussion Paper 2011-060, Tilburg University, Center for Economic Research.
    19. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    20. J. X. Cruz Neto & P. R. Oliveira & A. Soubeyran & J. C. O. Souza, 2020. "A generalized proximal linearized algorithm for DC functions with application to the optimal size of the firm problem," Annals of Operations Research, Springer, vol. 289(2), pages 313-339, June.

    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:86:y:2023:i:1:d:10.1007_s10898-022-01255-8. 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.