@inproceedings{66c8263355874af98cb4d2c8d6655cf0,

title = "A bound on the minimum rank of solutions to sparse linear matrix equations",

abstract = "We derive a new upper bound on the minimum rank of matrices belonging to an affine slice of the positive semidefinite cone, when the affine slice is defined according to a system of sparse linear matrix equations. It is shown that a feasible matrix whose rank is no greater than said bound can be computed in polynomial time. The bound depends on both the number of linear matrix equations and their underlying sparsity pattern. For certain problem families, this bound is shown to improve upon well known bounds in the literature. Several examples are provided to illustrate the efficacy of this bound.",

keywords = "Chordal graphs, Rank minimization, Semidefinite programming, Sparse linear matrix equations",

author = "Raphael Louca and Subhonmesh Bose and Eilyan Bitar",

note = "Funding Information: Supported in part by NSF grant ECCS-1351621, NSF grant CNS-1239178, US DoE under the CERTS initiative, PSERC under sub-award S-52, and a Postdoctoral Fellowship from the Atkinson Center for a Sustainable Future. Publisher Copyright: {\textcopyright} 2016 American Automatic Control Council (AACC).; 2016 American Control Conference, ACC 2016 ; Conference date: 06-07-2016 Through 08-07-2016",

year = "2016",

month = jul,

day = "28",

doi = "10.1109/ACC.2016.7526693",

language = "English (US)",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "6501--6506",

booktitle = "2016 American Control Conference, ACC 2016",

address = "United States",

}