IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v205y2025i3d10.1007_s10957-025-02644-1.html
   My bibliography  Save this article

Tight Error Bounds for Log-Determinant Cones Without Constraint Qualifications

Author

Listed:
  • Ying Lin

    (The Hong Kong Polytechnic University)

  • Scott B. Lindstrom

    (Curtin University)

  • Bruno F. Lourenço

    (Institute of Statistical Mathematics)

  • Ting Kei Pong

    (The Hong Kong Polytechnic University)

Abstract

In this paper, without requiring any constraint qualifications, we establish tight error bounds for the log-determinant cone, which is the closure of the hypograph of the perspective function of the log-determinant function. This error bound is obtained using the recently developed framework based on one-step facial residual functions.

Suggested Citation

  • Ying Lin & Scott B. Lindstrom & Bruno F. Lourenço & Ting Kei Pong, 2025. "Tight Error Bounds for Log-Determinant Cones Without Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 205(3), pages 1-42, June.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02644-1
    DOI: 10.1007/s10957-025-02644-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-025-02644-1
    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/s10957-025-02644-1?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. Hayato Waki & Masakazu Muramatsu, 2013. "Facial Reduction Algorithms for Conic Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 188-215, July.
    2. Chris Coey & Lea Kapelevich & Juan Pablo Vielma, 2022. "Solving Natural Conic Formulations with Hypatia.jl," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2686-2699, September.
    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. Ernest K. Ryu & Yanli Liu & Wotao Yin, 2019. "Douglas–Rachford splitting and ADMM for pathological convex optimization," Computational Optimization and Applications, Springer, vol. 74(3), pages 747-778, December.
    2. Yoshiyuki Sekiguchi & Hayato Waki, 2021. "Perturbation Analysis of Singular Semidefinite Programs and Its Applications to Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(1), pages 52-72, January.
    3. Yuzhu Wang & Akihiro Tanaka & Akiko Yoshise, 2021. "Polyhedral approximations of the semidefinite cone and their application," Computational Optimization and Applications, Springer, vol. 78(3), pages 893-913, April.
    4. Mathieu Besançon & Joaquim Dias Garcia & Benoît Legat & Akshay Sharma, 2024. "Flexible Differentiable Optimization via Model Transformations," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 456-478, March.
    5. David E. Bernal Neira & Ignacio E. Grossmann, 2024. "Convex mixed-integer nonlinear programs derived from generalized disjunctive programming using cones," Computational Optimization and Applications, Springer, vol. 88(1), pages 251-312, May.
    6. Lea Kapelevich & Erling D. Andersen & Juan Pablo Vielma, 2024. "Computing Conjugate Barrier Information for Nonsymmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 271-295, 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:joptap:v:205:y:2025:i:3:d:10.1007_s10957-025-02644-1. 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.