Proximal-stabilized semidefinite programming

Stefano Cipolla () and Jacek Gondzio ()
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Stefano Cipolla: University of Southampton School of Mathematical Sciences
Jacek Gondzio: The University of Edinburgh School of Mathematics and Maxwell Institute for Mathematical Sciences

Computational Optimization and Applications, 2025, vol. 91, issue 2, No 9, 573-616

Abstract: 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.

Keywords: Semidefinite programming; Interior point method; Proximal point methods; Primal–dual regularization; 90C22; 90C51; 90C46; 90C25; 49N15 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10589-024-00614-3

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