We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
MINIMUM-RANK POSITIVE SEMIDEFINITE MATRIX COMPLETION WITH CHORDAL PATTERNS AND APPLICATIONS TO SEMIDEFINITE RELAXATIONS.
- Authors
XIN JIANG; YIFAN SUN; ANDERSEN, MARTIN S.; VANDENBERGHE, LIEVEN
- Abstract
We present an algorithm for computing the minimum-rank positive semidefinite completion of a sparse matrix with a chordal sparsity pattern. This problem is tractable, in contrast to the minimumrank positive semidefinite completion problem for general sparsity patterns. We also present a similar algorithm for the Euclidean distance matrix completion with minimum embedding dimension. The two algorithms use efficient recursions over a clique tree associated with the chordal sparsity pattern. As an application, we use the minimum-rank completion method as a rounding technique to convert the solution of a sparse semidefinite optimization problem with non-unique solutions to an optimal solution of lower rank. In experiments with semidefinite relaxations of optimal power flow problems, the minimum-rank completion often results in solutions of lower rank than the solutions computed by interior-point solvers.
- Subjects
SEMIDEFINITE programming; GRAPH theory; COMPUTER algorithms; EUCLIDEAN distance; SPARSE matrix software
- Publication
Applied Set-Valued Analysis & Optimization, 2023, Vol 5, Issue 2, p265
- ISSN
2562-7775
- Publication type
Article
- DOI
10.23952/asvao.5.2023.2.10