{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JZI7LQXZMHOBN7QNP7GZGGAYWJ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ad2e59d5061252cfd374efab6b3fe155ec569fd94fb36ae8fd23f980515593a7","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-11T04:00:57Z","title_canon_sha256":"273b85112f3e759746d1114273834499207bc8af25683ed033e71e0f528f52c5"},"schema_version":"1.0","source":{"id":"1112.2318","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.2318","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1112.2318v2","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2318","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"JZI7LQXZMHOB","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JZI7LQXZMHOBN7QN","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JZI7LQXZ","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:1599b8da35be20789d24b6df6f0aa984ead240b9f4c65243b80b9972f5690be8","target":"graph","created_at":"2026-05-18T03:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a particular Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed ","authors_text":"B. Mishra, F. Bach, G. Meyer, R. Sepulchre","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-11T04:00:57Z","title":"Low-rank optimization with trace norm penalty"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2318","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0cfe51b7b7ac188230e38df1d9e16fd15a55d52b8fedf53862d6ab7102246817","target":"record","created_at":"2026-05-18T03:22:06Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ad2e59d5061252cfd374efab6b3fe155ec569fd94fb36ae8fd23f980515593a7","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-12-11T04:00:57Z","title_canon_sha256":"273b85112f3e759746d1114273834499207bc8af25683ed033e71e0f528f52c5"},"schema_version":"1.0","source":{"id":"1112.2318","kind":"arxiv","version":2}},"canonical_sha256":"4e51f5c2f961dc16fe0d7fcd931818b250b539cea54ae199006f3f06d7ed09b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e51f5c2f961dc16fe0d7fcd931818b250b539cea54ae199006f3f06d7ed09b5","first_computed_at":"2026-05-18T03:22:06.359382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:06.359382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GG2aUcwSlCK6g1zXwP19S1KsSyOCCQMGddIdybtLj/pw49NgjAgJP4VsKmF9RZNXvlkAHS3L6yWCHMKQYQfiCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:06.360028Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.2318","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cfe51b7b7ac188230e38df1d9e16fd15a55d52b8fedf53862d6ab7102246817","sha256:1599b8da35be20789d24b6df6f0aa984ead240b9f4c65243b80b9972f5690be8"],"state_sha256":"63713f6867dfa3459c6388f84a897ea75c7a0fff54e87ed5eb8eed5cf448db1c"}