{"paper":{"title":"Provable Burer-Monteiro factorization for a class of norm-constrained matrix problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.IT","cs.NA","math.IT","math.OC"],"primary_cat":"stat.ML","authors_text":"Anastasios Kyrillidis, Constantine Caramanis, Dohyung Park, Srinadh Bhojanapalli, Sujay Sanghavi","submitted_at":"2016-06-04T02:12:13Z","abstract_excerpt":"We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introduces non-convexity in the objective. We focus on constraint sets that include both positive semi-definite (PSD) constraints and specific matrix norm-constraints. Such criteria appear in quantum state tomography and phase retrieval applications.\n  We show that non-convex projected gradient descent favors local linear convergence in the factored space. We build our theory on a nov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01316","kind":"arxiv","version":3},"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"}