Sieve-SDP: a simple facial reduction algorithm to preprocess semidefinite programs

  • We introduce Sieve-SDP, a simple facial reduction algorithm to preprocess semidefinite programs (SDPs). Sieve-SDP inspects the constraints of the problem to detect lack of strict feasibility, deletes redundant rows and columns, and reduces the size of the variable matrix. It often detects infeasibility. It does not rely on any optimization solver: the only subroutine it needs is Cholesky factorization, hence it can be implemented in a few lines of code in machine precision. We present extensive computational results on several problem collections from the literature, with many SDPs coming from polynomial optimization.

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Metadaten
Author:Yuzixuan Zhu, Gábor Pataki, Quoc Tran-Dinh
DOI:https://doi.org/10.1007/s12532-019-00164-4
ISSN:1867-2949
Parent Title (English):Mathematical Programming Computation
Publisher:Springer Science and Business Media LLC
Document Type:Article
Language:English
Year of Completion:2019
Tag:Software; Theoretical Computer Science
Volume:11
Issue:3
Page Number:84
First Page:503
Last Page:586
Mathematical Programming Computation :MPC 2019 - Issue 3
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