Exploiting sparsity in semidefinite programming via matrix completion II: Implementation and numerical results

Kazuhide Nakata, Katsuki Fujisawa, Mituhiro Fukuda, Masakazu Kojima, Kazuo Murota

研究成果: Contribution to journalArticle査読

99 被引用数 (Scopus)

抄録

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 semidefinite 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 incorporating a positive definite matrix completion itself in a primal-dual interior-point method. The current article presents the details of their implementations. We introduce 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.

本文言語英語
ページ(範囲)303-327
ページ数25
ジャーナルMathematical Programming, Series B
95
2
DOI
出版ステータス出版済み - 2 1 2003
外部発表はい

All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 数学 (全般)

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