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This content will become publicly available on December 14, 2022

Title: Globally Convergent Low Complexity Algorithms for Semidefinite Programming
Semidefinite programs (SDP) are a staple of today’s systems theory, with applications ranging from robust control to systems identification. However, current state-of-the art solution methods have poor scaling properties, and thus are limited to relatively moderate size problems. Recently, several approximations have been proposed where the original SDP is relaxed to a sequence of lower complexity problems (such as linear programs (LPs) or second order cone programs (SOCPs)). While successful in many cases, there is no guarantee that these relaxations converge to the global optimum of the original program. Indeed, examples exists where these relaxations "get stuck" at suboptimal solutions. To circumvent this difficulty in this paper we propose an algorithm to solve SDPs based on solving a sequence of LPs or SOCPs, guaranteed to converge in a finite number of steps to an ε-suboptimal solution of the original problem. We further provide a bound on the number of steps required, as a function of ε and the problem data.
Authors:
;
Award ID(s):
1808381 2038493
Publication Date:
NSF-PAR ID:
10349424
Journal Name:
60th IEEE Conf. Decision and Control
Page Range or eLocation-ID:
1709 to 1714
Sponsoring Org:
National Science Foundation
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