IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v195y2022i1d10.1007_s10957-022-02082-3.html
   My bibliography  Save this article

Strong Duality for General Quadratic Programs with Quadratic Equality Constraints

Author

Listed:
  • Duy-Van Nguyen

    (University of Trier)

Abstract

In this article, by ‘general quadratic program’ we mean an optimization problem, in which all functions involved are quadratic or linear and local optima can be different from global optima. For a class of general quadratic optimization problems with quadratic equality constraints, the Lagrangian dual problem is constructed, which is a semi-infinite linear program, or equivalently, a copositive program, i.e., a conic program over the closed convex cone of copositive matrices. Solvability of both primal and dual problems and conditions for strong duality are then investigated in connection with some results from nonlinear parametric optimization.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02082-3
    DOI: 10.1007/s10957-022-02082-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-022-02082-3
    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/s10957-022-02082-3?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. Flippo, Olaf E. & Jansen, Benjamin, 1996. "Duality and sensitivity in nonconvex quadratic optimization over an ellipsoid," European Journal of Operational Research, Elsevier, vol. 94(1), pages 167-178, October.
    2. Joe-Mei Feng & Gang-Xuan Lin & Reuy-Lin Sheu & Yong Xia, 2012. "Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint," Journal of Global Optimization, Springer, vol. 54(2), pages 275-293, October.
    3. 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.
    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. Pinar, Mustafa C., 2000. "A simple duality proof in convex quadratic programming with a quadratic constraint, and some applications," European Journal of Operational Research, Elsevier, vol. 124(1), pages 151-158, July.
    3. A. Taati & M. Salahi, 2019. "A conjugate gradient-based algorithm for large-scale quadratic programming problem with one quadratic constraint," Computational Optimization and Applications, Springer, vol. 74(1), pages 195-223, September.
    4. Rujun Jiang & Man-Chung Yue & Zhishuo Zhou, 2021. "An accelerated first-order method with complexity analysis for solving cubic regularization subproblems," Computational Optimization and Applications, Springer, vol. 79(2), pages 471-506, June.
    5. Zhuoyi Xu & Yong Xia & Jiulin Wang, 2021. "Cheaper relaxation and better approximation for multi-ball constrained quadratic optimization and extension," Journal of Global Optimization, Springer, vol. 80(2), pages 341-356, June.
    6. Matamala, Yolanda & Feijoo, Felipe, 2021. "A two-stage stochastic Stackelberg model for microgrid operation with chance constraints for renewable energy generation uncertainty," Applied Energy, Elsevier, vol. 303(C).
    7. Ting Pong & Henry Wolkowicz, 2014. "The generalized trust region subproblem," Computational Optimization and Applications, Springer, vol. 58(2), pages 273-322, June.
    8. N.V. Thoai, 2002. "Convergence and Application of a Decomposition Method Using Duality Bounds for Nonconvex Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 165-193, April.

    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:195:y:2022:i:1:d:10.1007_s10957-022-02082-3. 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.