Name
Title | ||
|---|---|---|
Exploiting sparsity in semidefinite programming via matrix completion II: implementation and numerical results |
Abstract | ||
|---|---|---|
In Part I of this series of articles, we introduced a general framework of exploiting the aggregate sparsity pattern over all data matrices of large scale and sparse semidefi- nite programs (SDPs) when solving them by primal-dual interior-point methods. This framework is based on some results about positive semidefinite matrix completion, and it can be embodied in two different ways. One is by a conversion of a given sparse SDP having a large scale positive semidefinite matrix variable into an SDP having multiple but smaller positive semidefinite matrix variables. The other is by incor- porating a positive definite matrix completion itself in a primal-dual interior-point method. The current article presents the details of their implementations. We in- troduce new techniques to deal with the sparsity through a clique tree in the former method and through new computational formulae in the latter one. Numerical results over different classes of SDPs show that these methods can be very efficient for some problems. |
Year | DOI | Venue |
|---|---|---|
2003 | 10.1007/s10107-002-0351-9 | Math. Program. |
Keywords | Field | DocType |
General Framework,Data Matrice,Matrix Variable,Positive Semidefinite,Positive Definite Matrix | Discrete mathematics,Sparse PCA,Mathematical optimization,Matrix completion,Matrix (mathematics),Positive-definite matrix,Interior point method,Semidefinite embedding,Semidefinite programming,Mathematics,Sparse matrix | Journal |
Volume | Issue | ISSN |
95 | 2 | 0025-5610 |
Citations | PageRank | References |
32 | 3.07 | 8 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Kazuhide Nakata | 1 | 216 | 24.12 |
| Katsuki Fujisawa | 2 | 248 | 28.63 |
| Mituhiro Fukuda | 3 | 197 | 18.59 |
| Masakazu Kojima | 4 | 1603 | 222.51 |
| Kazuo Murota | 5 | 975 | 133.88 |