Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Distance Matrix Completion by Numerical Optimization
Computational Optimization and Applications
Journal of Global Optimization
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
Sensor network localization, euclidean distance matrix completions, and graph realization
Proceedings of the first ACM international workshop on Mobile entity localization and tracking in GPS-less environments
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
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Motivated by the molecular conformation problem, completions of partial Euclidian distance matrices are studied. It is proved that any partial distance matrix with a chordal graph can be completed to a distance matrix. Given any nonchordal graph $G$, it is shown that there is a partial distance matrix $A$ with graph $G$ such that $A$ does not admit any distance matrix completions. Finally, the connection between distance matrix completions and positive semidefinite completions is outlined.