Abstract
We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton's method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.
| Original language | English (US) |
|---|---|
| Article number | 946893 |
| Journal | Journal of Applied Mathematics |
| Volume | 2012 |
| DOIs | |
| State | Published - 2012 |
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ASJC Scopus subject areas
- Applied Mathematics
Cite this
An interior point method for solving semidefinite programs using cutting planes and weighted analytic centers. / MacHacek, John; Jibrin, Shafiu.
In: Journal of Applied Mathematics, Vol. 2012, 946893, 2012.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An interior point method for solving semidefinite programs using cutting planes and weighted analytic centers
AU - MacHacek, John
AU - Jibrin, Shafiu
PY - 2012
Y1 - 2012
N2 - We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton's method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.
AB - We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton's method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.
UR - http://www.scopus.com/inward/record.url?scp=84867828240&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84867828240&partnerID=8YFLogxK
U2 - 10.1155/2012/946893
DO - 10.1155/2012/946893
M3 - Article
AN - SCOPUS:84867828240
VL - 2012
JO - Journal of Applied Mathematics
JF - Journal of Applied Mathematics
SN - 1110-757X
M1 - 946893
ER -