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• W2795403780 abstract "This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices that are nonzero only on a principal submatrix. Also, the completion of an SOS matrix is equivalent to a set of SOS conditions on its principal submatrices and a consistency condition on the Gram representation of the principal submatrices. These results are partial extensions of chordal decomposition and completion of scalar matrices to matrices with polynomial entries. We apply the SOS decomposition result to exploit sparsity in matrix-valued SOS programs. Numerical results demonstrate the high potential of this approach for solving large-scale sparse matrix-valued SOS programs." @default.
• W2795403780 created "2018-04-13" @default.
• W2795403780 creator A5002663383 @default.
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• W2795403780 date "2018-12-01" @default.
• W2795403780 modified "2023-09-26" @default.
• W2795403780 title "Decomposition and Completion of Sum-of-Squares Matrices" @default.
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• W2795403780 doi "https://doi.org/10.1109/cdc.2018.8619144" @default.
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