TY - JOUR
T1 - A facial reduction algorithm for finding sparse SOS representations
AU - Waki, Hayato
AU - Muramatsu, Masakazu
N1 - Funding Information:
We thank Dr. Johan Löfberg for his comments. The first author was supported by Grant-in-Aid for JSPS Fellow 20003236 . The second author was partially supported by Grant-in-Aid for Scientific Research (C) 19560063 .
PY - 2010/9
Y1 - 2010/9
N2 - 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) 4562] 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.
AB - 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) 4562] 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.
UR - http://www.scopus.com/inward/record.url?scp=77956338949&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956338949&partnerID=8YFLogxK
U2 - 10.1016/j.orl.2010.05.011
DO - 10.1016/j.orl.2010.05.011
M3 - Article
AN - SCOPUS:77956338949
VL - 38
SP - 361
EP - 365
JO - Operations Research Letters
JF - Operations Research Letters
SN - 0167-6377
IS - 5
ER -