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An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones

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  • Yuwen Chen

    (University of Oxford)

  • Paul Goulart

    (University of Oxford)

Abstract

We present an implementation of interior-point methods for generalized power cones, power mean cones and relative entropy cones, by exploiting underlying low-rank and sparsity properties of the Hessians of their logarithmically homogeneous self-concordant barrier functions. We prove that the augmented linear system in our interior-point method can be sparse and quasidefinite after adding a static regularization term, enabling the use of sparse LDL factorization for nonsymmetric cones. Numerical results show that our implementation can exploit sparsity in our test examples.

Suggested Citation

  • Yuwen Chen & Paul Goulart, 2025. "An Efficient Implementation of Interior-Point Methods for a Class of Nonsymmetric Cones," Journal of Optimization Theory and Applications, Springer, vol. 204(2), pages 1-28, February.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:2:d:10.1007_s10957-024-02573-5
    DOI: 10.1007/s10957-024-02573-5
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    References listed on IDEAS

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    1. Yu. E. Nesterov & M. J. Todd, 1997. "Self-Scaled Barriers and Interior-Point Methods for Convex Programming," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 1-42, February.
    2. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
    3. Michael Garstka & Mark Cannon & Paul Goulart, 2021. "COSMO: A Conic Operator Splitting Method for Convex Conic Problems," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 779-810, September.
    Full references (including those not matched with items on IDEAS)

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