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) 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.
| Original language | English |
|---|---|
| Pages (from-to) | 361-365 |
| Number of pages | 5 |
| Journal | Operations Research Letters |
| Volume | 38 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Sep 1 2010 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Software
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics
Cite this
A facial reduction algorithm for finding sparse SOS representations. / Waki, Hayato; Muramatsu, Masakazu.
In: Operations Research Letters, Vol. 38, No. 5, 01.09.2010, p. 361-365.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A facial reduction algorithm for finding sparse SOS representations
AU - Waki, Hayato
AU - Muramatsu, Masakazu
PY - 2010/9/1
Y1 - 2010/9/1
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.
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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 -