Coordinate Shadows of Semidefinite and Euclidean Distance Matrices
研究了半定矩阵锥和欧几里得距离矩阵锥在部分矩阵元素上的投影，分类了这些投影何时是闭集，并利用其边界结构解释了Krislock-Wolkowicz面约简算法，揭示了弦图假设下最小锥的组合刻画。
We consider the projected semidefinite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semidefinite 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 by-product, 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.