Proximal-stabilized semidefinite programming
Proximal-stabilized semidefinite programming
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.
49N15, 90C22, 90C25, 90C46, 90C51, Interior point method, Primal–dual regularization, Proximal point methods, Semidefinite programming
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Gondzio, Jacek
83e55b47-99a9-4f07-bbd0-79258ce12830
Cipolla, Stefano
373fdd4b-520f-485c-b36d-f75ce33d4e05
Gondzio, Jacek
83e55b47-99a9-4f07-bbd0-79258ce12830
Cipolla, Stefano and Gondzio, Jacek
(2024)
Proximal-stabilized semidefinite programming.
Computational Optimization and Applications.
(doi:10.1007/s10589-024-00614-3).
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.
Text
s10589-024-00614-3
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Accepted/In Press date: 3 October 2024
e-pub ahead of print date: 14 October 2024
Keywords:
49N15, 90C22, 90C25, 90C46, 90C51, Interior point method, Primal–dual regularization, Proximal point methods, Semidefinite programming
Identifiers
Local EPrints ID: 495709
URI: http://eprints.soton.ac.uk/id/eprint/495709
ISSN: 0926-6003
PURE UUID: 4264b783-0d92-43ca-ba12-4b8d6ed2e1e1
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Date deposited: 20 Nov 2024 17:51
Last modified: 21 Nov 2024 03:08
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Author:
Stefano Cipolla
Author:
Jacek Gondzio
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