Abstract
We propose a method to reduce the sizes of SDP relaxation problems fur a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [8] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this method is a partial application of a facial reduction algorithm, which generates a smaller SDP problem with an interior feasible solution. In general, SDP relaxation problems for POPs often become highly degenerate because of a lack of interior feasible solutions. As a result, the resulting SDP relaxation problems obtained by this method may have an interior feasible solution, and one may be able to solve the SDP relaxation problems effectively Numerical results in this paper show that the resulting SDP relaxation problems obtained by this method can be solved fast and accurately.
| Original language | English |
|---|---|
| Pages (from-to) | 161-190 |
| Number of pages | 30 |
| Journal | Journal of the Operations Research Society of Japan |
| Volume | 54 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 2011 |
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All Science Journal Classification (ASJC) codes
- Decision Sciences(all)
- Management Science and Operations Research
Cite this
An extension of the elimination method for a sparse sos polynomial. / Waki, Hayato; Muramatsu, Masakazu.
In: Journal of the Operations Research Society of Japan, Vol. 54, No. 4, 12.2011, p. 161-190.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An extension of the elimination method for a sparse sos polynomial
AU - Waki, Hayato
AU - Muramatsu, Masakazu
PY - 2011/12
Y1 - 2011/12
N2 - We propose a method to reduce the sizes of SDP relaxation problems fur a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [8] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this method is a partial application of a facial reduction algorithm, which generates a smaller SDP problem with an interior feasible solution. In general, SDP relaxation problems for POPs often become highly degenerate because of a lack of interior feasible solutions. As a result, the resulting SDP relaxation problems obtained by this method may have an interior feasible solution, and one may be able to solve the SDP relaxation problems effectively Numerical results in this paper show that the resulting SDP relaxation problems obtained by this method can be solved fast and accurately.
AB - We propose a method to reduce the sizes of SDP relaxation problems fur a given polynomial optimization problem (POP). This method is an extension of the elimination method for a sparse SOS polynomial in [8] and exploits sparsity of polynomials involved in a given POP. In addition, we show that this method is a partial application of a facial reduction algorithm, which generates a smaller SDP problem with an interior feasible solution. In general, SDP relaxation problems for POPs often become highly degenerate because of a lack of interior feasible solutions. As a result, the resulting SDP relaxation problems obtained by this method may have an interior feasible solution, and one may be able to solve the SDP relaxation problems effectively Numerical results in this paper show that the resulting SDP relaxation problems obtained by this method can be solved fast and accurately.
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UR - http://www.scopus.com/inward/citedby.url?scp=84878798556&partnerID=8YFLogxK
U2 - 10.15807/jorsj.54.161
DO - 10.15807/jorsj.54.161
M3 - Article
AN - SCOPUS:84878798556
VL - 54
SP - 161
EP - 190
JO - Journal of the Operations Research Society of Japan
JF - Journal of the Operations Research Society of Japan
SN - 0453-4514
IS - 4
ER -