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Proximal-stabilized semidefinite programming

Author

Listed:
  • Stefano Cipolla

    (University of Southampton School of Mathematical Sciences)

  • Jacek Gondzio

    (The University of Edinburgh School of Mathematics and Maxwell Institute for Mathematical Sciences)

Abstract

A regularized version of the primal-dual Interior Point Method (IPM) for the solution of Semidefinite Programming Problems (SDPs) is presented in this paper. Leveraging on the proximal point method, a novel Proximal Stabilized Interior Point Method for SDP (PS-SDP-IPM) is introduced. The method is strongly supported by theoretical results concerning its convergence: the worst-case complexity result is established for the inner regularized infeasible inexact IPM solver. The new method demonstrates an increased robustness when dealing with problems characterized by ill-conditioning or linear dependence of the constraints without requiring any kind of pre-processing. Extensive numerical experience is reported to illustrate advantages of the proposed method when compared to the state-of-the-art solver.

Suggested Citation

  • Stefano Cipolla & Jacek Gondzio, 2025. "Proximal-stabilized semidefinite programming," Computational Optimization and Applications, Springer, vol. 91(2), pages 573-616, June.
    • Handle: RePEc:spr:coopap:v:91:y:2025:i:2:d:10.1007_s10589-024-00614-3
    DOI: 10.1007/s10589-024-00614-3
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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. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    3. Spyridon Pougkakiotis & Jacek Gondzio, 2022. "An Interior Point-Proximal Method of Multipliers for Linear Positive Semi-Definite Programming," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 97-129, January.
    4. Cipolla, S. & Gondzio, J. & Zanetti, F., 2024. "A regularized interior point method for sparse optimal transport on graphs," European Journal of Operational Research, Elsevier, vol. 319(2), pages 413-426.
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