{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:33XM7LGCG5DO7EMECCO6XPOKM7","short_pith_number":"pith:33XM7LGC","schema_version":"1.0","canonical_sha256":"deeecfacc23746ef9184109debbdca67def5fd84cad450c667c7320ce0f26a3b","source":{"kind":"arxiv","id":"1606.02116","version":6},"attestation_state":"computed","paper":{"title":"Local Convergence Properties of Douglas--Rachford and ADMM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabriel Peyr\\'e, Jalal Fadili, Jingwei Liang","submitted_at":"2016-06-07T12:25:38Z","abstract_excerpt":"The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of DR/ADMM when the involved functions are moreover partly smooth. More precisely, when the two functions are partly smooth relative to their respective smooth submanifolds, we show that DR/ADMM (i) identifies these manifolds in finite time; (ii) enters a local linear conv"},"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":"1606.02116","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-06-07T12:25:38Z","cross_cats_sorted":[],"title_canon_sha256":"8b7d81dd12389bf2df966d94a1cebe7056265cc7efd40f1acf528f1a4a3ce797","abstract_canon_sha256":"b405d908800211986b731d7f079483e3a9c18a13ec5c785a795c5a830e3cb134"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:32.478562Z","signature_b64":"sYlKq1vEi5nx3pTCCwtXn53hxM1rK2wQyHvWZaLuhc6dGvjWN+8DKxXmeeCGjTGfsTMkTjRM6Oc90o5FUqJeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"deeecfacc23746ef9184109debbdca67def5fd84cad450c667c7320ce0f26a3b","last_reissued_at":"2026-05-18T00:49:32.477841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:32.477841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local Convergence Properties of Douglas--Rachford and ADMM","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gabriel Peyr\\'e, Jalal Fadili, Jingwei Liang","submitted_at":"2016-06-07T12:25:38Z","abstract_excerpt":"The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local linear convergence behaviour of DR/ADMM when the involved functions are moreover partly smooth. More precisely, when the two functions are partly smooth relative to their respective smooth submanifolds, we show that DR/ADMM (i) identifies these manifolds in finite time; (ii) enters a local linear conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02116","kind":"arxiv","version":6},"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":"1606.02116","created_at":"2026-05-18T00:49:32.477954+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.02116v6","created_at":"2026-05-18T00:49:32.477954+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02116","created_at":"2026-05-18T00:49:32.477954+00:00"},{"alias_kind":"pith_short_12","alias_value":"33XM7LGCG5DO","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"33XM7LGCG5DO7EME","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"33XM7LGC","created_at":"2026-05-18T12:29:55.572404+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/33XM7LGCG5DO7EMECCO6XPOKM7","json":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7.json","graph_json":"https://pith.science/api/pith-number/33XM7LGCG5DO7EMECCO6XPOKM7/graph.json","events_json":"https://pith.science/api/pith-number/33XM7LGCG5DO7EMECCO6XPOKM7/events.json","paper":"https://pith.science/paper/33XM7LGC"},"agent_actions":{"view_html":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7","download_json":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7.json","view_paper":"https://pith.science/paper/33XM7LGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.02116&json=true","fetch_graph":"https://pith.science/api/pith-number/33XM7LGCG5DO7EMECCO6XPOKM7/graph.json","fetch_events":"https://pith.science/api/pith-number/33XM7LGCG5DO7EMECCO6XPOKM7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7/action/storage_attestation","attest_author":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7/action/author_attestation","sign_citation":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7/action/citation_signature","submit_replication":"https://pith.science/pith/33XM7LGCG5DO7EMECCO6XPOKM7/action/replication_record"}},"created_at":"2026-05-18T00:49:32.477954+00:00","updated_at":"2026-05-18T00:49:32.477954+00:00"}