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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
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    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)

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