IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v90y2025i1d10.1007_s10589-024-00617-0.html
   My bibliography  Save this article

A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients

Author

Listed:
  • Jie Wang

    (Chinese Academy of Sciences)

  • Victor Magron

    (LAAS CNRS & IMT)

Abstract

This paper proposes a real moment-HSOS hierarchy for complex polynomial optimization problems with real coefficients. We show that this hierarchy provides the same sequence of lower bounds as the complex analogue, yet is much cheaper to solve. In addition, we prove that global optimality is achieved when the ranks of the moment matrix and certain submatrix equal two in case that a sphere constraint is present, and as a consequence, the complex polynomial optimization problem has either two real optimal solutions or a pair of conjugate optimal solutions. A simple procedure for extracting a pair of conjugate optimal solutions is given in the latter case. Various numerical examples are presented to demonstrate the efficiency of this new hierarchy, and an application to polyphase code design is also provided.

Suggested Citation

  • Jie Wang & Victor Magron, 2025. "A real moment-HSOS hierarchy for complex polynomial optimization with real coefficients," Computational Optimization and Applications, Springer, vol. 90(1), pages 53-75, January.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:1:d:10.1007_s10589-024-00617-0
    DOI: 10.1007/s10589-024-00617-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-024-00617-0
    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/s10589-024-00617-0?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. Dan Bienstock & Mauro Escobar & Claudio Gentile & Leo Liberti, 2020. "Mathematical programming formulations for the alternating current optimal power flow problem," 4OR, Springer, vol. 18(3), pages 249-292, September.
    2. Jie Wang & Victor Magron, 2022. "Exploiting Sparsity in Complex Polynomial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 335-359, January.
    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. Yves Crama & Michel Grabisch & Silvano Martello, 2022. "Preface," Annals of Operations Research, Springer, vol. 314(1), pages 1-3, July.
    2. Yves Crama & Michel Grabisch & Silvano Martello, 2021. "4OR comes of age," 4OR, Springer, vol. 19(1), pages 1-13, March.
    3. Yves Crama & Michel Grabisch & Silvano Martello, 2024. "Still more surveys in operations research…," Annals of Operations Research, Springer, vol. 343(2), pages 559-571, December.
    4. Bichler, Martin & Knörr, Johannes, 2023. "Getting prices right on electricity spot markets: On the economic impact of advanced power flow models," Energy Economics, Elsevier, vol. 126(C).
    5. Jens Hönen & Johann L. Hurink & Bert Zwart, 2023. "A classification scheme for local energy trading," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 85-118, March.
    6. Dimitri J. Papageorgiou, 2025. "Data-Driven Distributionally Robust Optimization for Long-Term Contract vs. Spot Allocation Decisions: Application to Electricity Markets," Papers 2501.15340, arXiv.org.
    7. Sander Claeys & Marta Vanin & Frederik Geth & Geert Deconinck, 2021. "Applications of optimization models for electricity distribution networks," Wiley Interdisciplinary Reviews: Energy and Environment, Wiley Blackwell, vol. 10(5), September.
    8. Jie Wang & Victor Magron, 2022. "Exploiting Sparsity in Complex Polynomial Optimization," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 335-359, January.
    9. Kevin-Martin Aigner & Robert Burlacu & Frauke Liers & Alexander Martin, 2023. "Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 458-474, March.
    10. Sinjorgo, Lennart & Sotirov, Renata & Anjos, M.F., 2024. "Cuts and semidefinite liftings for the complex cut polytope," Other publications TiSEM e99ba505-f4f2-4b3c-a6b5-2, Tilburg University, School of Economics and Management.
    11. Cheng Lu & Zhibin Deng & Shu-Cherng Fang & Wenxun Xing, 2023. "A New Global Algorithm for Max-Cut Problem with Chordal Sparsity," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 608-638, May.
    12. Daniel Bienstock & Mauro Escobar & Claudio Gentile & Leo Liberti, 2022. "Mathematical programming formulations for the alternating current optimal power flow problem," Annals of Operations Research, Springer, vol. 314(1), pages 277-315, July.

    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:coopap:v:90:y:2025:i:1:d:10.1007_s10589-024-00617-0. 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.