{"paper":{"title":"Coordinate shadows of semi-definite and Euclidean distance matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"D. Drusvyatskiy, G. Pataki, H. Wolkowicz","submitted_at":"2014-05-08T18:35:04Z","abstract_excerpt":"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 gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2037","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}