{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:JTELTKKM4HNDRQNRX5FLDEXIJQ","short_pith_number":"pith:JTELTKKM","schema_version":"1.0","canonical_sha256":"4cc8b9a94ce1da38c1b1bf4ab192e84c246e903ab535cc83f2be8b367f9bc1ad","source":{"kind":"arxiv","id":"1608.04168","version":1},"attestation_state":"computed","paper":{"title":"Low-Rank Matrix Completion using Nuclear Norm with Facial Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Henry Wolkowicz, Shimeng Huang","submitted_at":"2016-08-15T01:48:19Z","abstract_excerpt":"Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite programming problem, (SDP). The SDP and its dual are regular in the sense that they both satisfy strict feasibility. Interior point algorithms are the current methods of choice for these problems. This means that it is difficult to solve large scale problems and difficult to get high accuracy solutions.\n  In this paper we take advantage of the structure at opt"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.04168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-08-15T01:48:19Z","cross_cats_sorted":[],"title_canon_sha256":"ebf505817ff6018eae64d549afff18293d358347cd85107d6d08ba436a2fcd71","abstract_canon_sha256":"0e4e4f28c661a7c5f6baa1c625b2bbd4307399df2c00052605e43630f38e615e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:04.144056Z","signature_b64":"UnlGfZxgCJhXIId7+H3HmsRRaQC1UXdFf5EJ4+m2lkUxKBKpXrd8Dr74GDQkka3aY8jRaNvwliDRnwnGQNcHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cc8b9a94ce1da38c1b1bf4ab192e84c246e903ab535cc83f2be8b367f9bc1ad","last_reissued_at":"2026-05-18T01:09:04.143643Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:04.143643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Low-Rank Matrix Completion using Nuclear Norm with Facial Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Henry Wolkowicz, Shimeng Huang","submitted_at":"2016-08-15T01:48:19Z","abstract_excerpt":"Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite programming problem, (SDP). The SDP and its dual are regular in the sense that they both satisfy strict feasibility. Interior point algorithms are the current methods of choice for these problems. This means that it is difficult to solve large scale problems and difficult to get high accuracy solutions.\n  In this paper we take advantage of the structure at opt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04168","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.04168","created_at":"2026-05-18T01:09:04.143706+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.04168v1","created_at":"2026-05-18T01:09:04.143706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04168","created_at":"2026-05-18T01:09:04.143706+00:00"},{"alias_kind":"pith_short_12","alias_value":"JTELTKKM4HND","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_16","alias_value":"JTELTKKM4HNDRQNR","created_at":"2026-05-18T12:30:25.849896+00:00"},{"alias_kind":"pith_short_8","alias_value":"JTELTKKM","created_at":"2026-05-18T12:30:25.849896+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ","json":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ.json","graph_json":"https://pith.science/api/pith-number/JTELTKKM4HNDRQNRX5FLDEXIJQ/graph.json","events_json":"https://pith.science/api/pith-number/JTELTKKM4HNDRQNRX5FLDEXIJQ/events.json","paper":"https://pith.science/paper/JTELTKKM"},"agent_actions":{"view_html":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ","download_json":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ.json","view_paper":"https://pith.science/paper/JTELTKKM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.04168&json=true","fetch_graph":"https://pith.science/api/pith-number/JTELTKKM4HNDRQNRX5FLDEXIJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/JTELTKKM4HNDRQNRX5FLDEXIJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ/action/storage_attestation","attest_author":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ/action/author_attestation","sign_citation":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ/action/citation_signature","submit_replication":"https://pith.science/pith/JTELTKKM4HNDRQNRX5FLDEXIJQ/action/replication_record"}},"created_at":"2026-05-18T01:09:04.143706+00:00","updated_at":"2026-05-18T01:09:04.143706+00:00"}