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arXiv · 1405.2037

Coordinate shadows of semi-definite and Euclidean distance matrices

D. Drusvyatskiy·G. Pataki·H. Wolkowicz
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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 classify 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. As a byproduct, we record a striking relationship between the complexity of the general facial reduction algorithm (singularity degree) and facial exposedness of conic images under a linear mapping.

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D. Drusvyatskiy, G. Pataki, H. Wolkowicz. 2014-05-08. Coordinate shadows of semi-definite and Euclidean distance matrices. https://arxiv.org/abs/1405.2037

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