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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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