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Coordinate shadows of semi-definite and Euclidean distance matrices

Dmitriy Drusvyatskiy (ddrusv***at***uw.edu)
Gabor Pataki (gabor***at***unc.edu)
Henry Wolkowicz (hwolkowicz***at***uwaterloo.ca)

Abstract: We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We characterize when these sets are closed, and use the boundary structure of these two sets to elucidate the Krislock-Wolkowicz facial reduction algorithm. In particular, we show that under a chordality assumption, the ``minimal cones'' of these problems admit combinatorial characterizations.

Keywords: Matrix completion, semidefinite programming, Euclidean distance matrices, facial reduction, Slater condition, projection, closedness

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 05/07/2014
Entry Accepted: 05/07/2014
Entry Last Modified: 01/08/2015

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