IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v194y2022i1d10.1007_s10957-022-02018-x.html
   My bibliography  Save this article

On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints

Author

Listed:
  • Temadher A. Almaadeed

    (Qatar University)

  • Saeid Ansary Karbasy

    (University of Guilan)

  • Maziar Salahi

    (University of Guilan)

  • Abdelouahed Hamdi

    (Qatar University)

Abstract

In this paper, we study the minimization of an indefinite quadratic function over the intersection of balls and linear inequality constraints (QOBL). Using the hyperplanes induced by the intersection of each pair of balls, we show that the optimal solution of QOBL can be found by solving several extended trust-region subproblems (e-TRS). To solve e-TRS, we use the alternating direction method of multipliers approach and a branch and bound algorithm. Numerical experiments show the efficiency of the proposed approach compared to the CVX and the extended adaptive ellipsoid-based algorithm.

Suggested Citation

  • Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02018-x
    DOI: 10.1007/s10957-022-02018-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02018-x
    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/s10957-022-02018-x?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. Maziar Salahi & Akram Taati & Henry Wolkowicz, 2017. "Local nonglobal minima for solving large-scale extended trust-region subproblems," Computational Optimization and Applications, Springer, vol. 66(2), pages 223-244, March.
    2. Davood Hajinezhad & Qingjiang Shi, 2018. "Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications," Journal of Global Optimization, Springer, vol. 70(1), pages 261-288, January.
    3. Lijun Xu & Bo Yu & Yin Zhang, 2017. "An alternating direction and projection algorithm for structure-enforced matrix factorization," Computational Optimization and Applications, Springer, vol. 68(2), pages 333-362, November.
    4. Amir Beck & Dror Pan, 2017. "A branch and bound algorithm for nonconvex quadratic optimization with ball and linear constraints," Journal of Global Optimization, Springer, vol. 69(2), pages 309-342, October.
    5. Mohammad Keyanpour & Naser Osmanpour, 2018. "On solving quadratically constrained quadratic programming problem with one non-convex constraint," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 320-336, June.
    6. 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.
    7. NESTEROV, Yu. & WOLKOWICZ, Henry & YE, Yinyu, 2000. "Semidefinite programming relaxations of nonconvex quadratic optimization," LIDAM Reprints CORE 1471, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. 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.
    2. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Discussion Paper 2006-85, Tilburg University, Center for Economic Research.
    3. Dolgopolik, Maksim V., 2021. "The alternating direction method of multipliers for finding the distance between ellipsoids," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. 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.
    5. Zhiqing Meng & Min Jiang & Rui Shen & Leiyan Xu & Chuangyin Dang, 2021. "An objective penalty function method for biconvex programming," Journal of Global Optimization, Springer, vol. 81(3), pages 599-620, November.
    6. Etienne Klerk, 2008. "The complexity of optimizing over a simplex, hypercube or sphere: a short survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 111-125, June.
    7. 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.
    8. Sebastián Arpón & Tito Homem-de-Mello & Bernardo K. Pagnoncelli, 2020. "An ADMM algorithm for two-stage stochastic programming problems," Annals of Operations Research, Springer, vol. 286(1), pages 559-582, March.
    9. Jianzhe Zhen & Ahmadreza Marandi & Danique de Moor & Dick den Hertog & Lieven Vandenberghe, 2022. "Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2410-2427, September.
    10. Yichuan Ding & Dongdong Ge & Henry Wolkowicz, 2011. "On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 88-104, February.
    11. M. Locatelli, 2023. "KKT-based primal-dual exactness conditions for the Shor relaxation," Journal of Global Optimization, Springer, vol. 86(2), pages 285-301, June.
    12. Nadav Hallak & Marc Teboulle, 2020. "Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 480-503, August.
    13. Marandi, Ahmadreza, 2017. "Aspects of quadratic optimization - nonconvexity, uncertainty, and applications," Other publications TiSEM d2b9c576-7128-4ee4-939a-7, Tilburg University, School of Economics and Management.
    14. Boris Defourny & Ilya O. Ryzhov & Warren B. Powell, 2015. "Optimal Information Blending with Measurements in the L 2 Sphere," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1060-1088, October.
    15. de Klerk, E., 2006. "The Complexity of Optimizing over a Simplex, Hypercube or Sphere : A Short Survey," Other publications TiSEM 88640b6d-5240-472d-8669-4, Tilburg University, School of Economics and Management.
    16. Utsav Sadana & Erick Delage, 2023. "The Value of Randomized Strategies in Distributionally Robust Risk-Averse Network Interdiction Problems," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 216-232, January.
    17. Santi, Éverton & Aloise, Daniel & Blanchard, Simon J., 2016. "A model for clustering data from heterogeneous dissimilarities," European Journal of Operational Research, Elsevier, vol. 253(3), pages 659-672.
    18. V. Jeyakumar & Guoyin Li, 2011. "Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems," Journal of Global Optimization, Springer, vol. 49(1), pages 1-14, January.
    19. Jiulin Wang & Mengmeng Song & Yong Xia, 2022. "On Local Nonglobal Minimum of Trust-Region Subproblem and Extension," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 707-722, November.
    20. Marcia Fampa & Jon Lee & Wendel Melo, 2017. "On global optimization with indefinite quadratics," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(3), pages 309-337, 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:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02018-x. 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.