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Computing Conjugate Barrier Information for Nonsymmetric Cones

Author

Listed:
  • Lea Kapelevich

    (MIT)

  • Erling D. Andersen

    (MOSEK ApS)

  • Juan Pablo Vielma

    (Google Research and MIT Sloan School of Management)

Abstract

The recent interior point algorithm by Dahl and Andersen [10] for nonsymmetric cones as well as earlier works [18, 21] require derivative information from the conjugate of the barrier function of the cones in the problem. Besides a few special cases, there is no indication of when this information is efficient to evaluate. We show how to compute the gradient of the conjugate barrier function for seven useful nonsymmetric cones. In some cases, this is helpful for deriving closed-form expressions for the inverse Hessian operator for the primal barrier.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02076-1
    DOI: 10.1007/s10957-022-02076-1
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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. 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.
    3. Dávid Papp & Sercan Yıldız, 2022. "Alfonso: Matlab Package for Nonsymmetric Conic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 11-19, January.
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