A facial reduction algorithm for finding sparse SOS representations

Authors:
Hayato Waki;Masakazu Muramatsu
Affiliations:
Department of Computer Science, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan;Department of Computer Science, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo, 182-8585, Japan
Venue:
Operations Research Letters
Year:
2010

Citing 6
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Abstract

The facial reduction algorithm reduces the size of the positive semidefinite cone in SDP. The elimination method for a sparse SOS polynomial [M. Kojima, S. Kim, H. Waki, Sparsity in sums of squares of polynomials, Math. Program. 103 (2005) 45-62] removes monomials which do not appear in any SOS representations. In this paper, we establish a relationship between a facial reduction algorithm and the elimination method for a sparse SOS polynomial.