TY - JOUR
T1 - Preprocessing sparse semidefinite programs via matrix completion
AU - Fujisawa, Katsuki
AU - Fukuda, Mituhiro
AU - Nakata, Kazuhide
N1 - Funding Information:
M. Fukuda is grateful for funding from the National Science Foundation (NSF) via Grant No. ITR-DMS 0113852, and also to Douglas N. Arnold and Masakazu Kojima from the Institute for Mathematics and its Applications and Tokyo Institute of Technology for inviting him as a visiting researcher at their respective institutes, making this research possible. In particular, Masakazu Kojima contributed many valuable comments on this article. The authors would like to thank Shigeru Mase from Tokyo Institute of Technology and Makoto Yamashita from Kanagawa University for suggesting the use of ANOVA. They are grateful to Takashi Tsuchiya from The Institute of Statistical Mathematics for pointing out ref. [l7]. Finally, they thank the two anonymous referees and Michael L. Overton of New York University for improving the clarity of the article.
PY - 2006/2
Y1 - 2006/2
N2 - Considering that preprocessing is an important phase in linear programing, it should be more systematically incorporated in semidefinite programing (SDP) solvers. The conversion method proposed by the authors [Fukuda, M., Kojima, M., Murota, K. and Nakata, K., 2000, SIAM Journal on Optimization , 11, 647-674 and Nakata, K., Fujisawa, K., Fukuda, M., Kojima, M. and Murota, K., 2003, Mathematical Programming (Series B) , 95, 303-327] is a preprocessing method for sparse SDPs based on matrix completion. This article proposed a new version of the conversion method, which employs a flop estimation function inside its heuristic procedure. Extensive numerical experiments are included showing the advantage of preprocessing by the conversion method for certain classes of very sparse SDPs.
AB - Considering that preprocessing is an important phase in linear programing, it should be more systematically incorporated in semidefinite programing (SDP) solvers. The conversion method proposed by the authors [Fukuda, M., Kojima, M., Murota, K. and Nakata, K., 2000, SIAM Journal on Optimization , 11, 647-674 and Nakata, K., Fujisawa, K., Fukuda, M., Kojima, M. and Murota, K., 2003, Mathematical Programming (Series B) , 95, 303-327] is a preprocessing method for sparse SDPs based on matrix completion. This article proposed a new version of the conversion method, which employs a flop estimation function inside its heuristic procedure. Extensive numerical experiments are included showing the advantage of preprocessing by the conversion method for certain classes of very sparse SDPs.
UR - http://www.scopus.com/inward/record.url?scp=29644433353&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=29644433353&partnerID=8YFLogxK
U2 - 10.1080/10556780512331319523
DO - 10.1080/10556780512331319523
M3 - Article
AN - SCOPUS:29644433353
SN - 1055-6788
VL - 21
SP - 17
EP - 39
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 1
ER -