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COSMO: A Conic Operator Splitting Method for Convex Conic Problems

Author

Listed:
  • Michael Garstka

    (University of Oxford)

  • Mark Cannon

    (University of Oxford)

  • Paul Goulart

    (University of Oxford)

Abstract

This paper describes the conic operator splitting method (COSMO) solver, an operator splitting algorithm and associated software package for convex optimisation problems with quadratic objective function and conic constraints. At each step, the algorithm alternates between solving a quasi-definite linear system with a constant coefficient matrix and a projection onto convex sets. The low per-iteration computational cost makes the method particularly efficient for large problems, e.g. semidefinite programs that arise in portfolio optimisation, graph theory, and robust control. Moreover, the solver uses chordal decomposition techniques and a new clique merging algorithm to effectively exploit sparsity in large, structured semidefinite programs. Numerical comparisons with other state-of-the-art solvers for a variety of benchmark problems show the effectiveness of our approach. Our Julia implementation is open source, designed to be extended and customised by the user, and is integrated into the Julia optimisation ecosystem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01896-x
    DOI: 10.1007/s10957-021-01896-x
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Rubio-García, Álvaro & Fernández-Lorenzo, Samuel & García-Ripoll, Juan José & Porras, Diego, 2024. "Accurate solution of the Index Tracking problem with a hybrid simulated annealing algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 639(C).
    3. Nikitas Rontsis & Paul Goulart & Yuji Nakatsukasa, 2022. "Efficient Semidefinite Programming with Approximate ADMM," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 292-320, January.

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