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Volume 5, Issue 2, 1 August 2023, Pages 265-283
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 minimum-rank 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.
How to Cite this Article:
X. Jiang, Y. Sun, M.S. Andersen, L. Vandenberghe, Minimum-rank positive semidefinite matrix completion with chordal patterns and applications to semidefinite relaxations, Appl. Set-Valued Anal. Optim. 5 (2023), 265-283.