{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XKYH5PWOUR544QMNKTTLNDQA2V","short_pith_number":"pith:XKYH5PWO","schema_version":"1.0","canonical_sha256":"bab07ebecea47bce418d54e6b68e00d56793a87d1eaba63dedced9cb7cc86aca","source":{"kind":"arxiv","id":"1807.00110","version":2},"attestation_state":"computed","paper":{"title":"Linear and sublinear convergence rates for a subdifferentiable distributed deterministic asynchronous Dykstra's algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"C.H. Jeffrey Pang","submitted_at":"2018-06-30T02:19:22Z","abstract_excerpt":"In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or block coordinate dual ascent. Each node in the distributed optimization problem is the sum of a known regularizing quadratic and a function to be minimized. In this paper, we prove sublinear convergence rates for the general algorithm, and a linear rate of convergence if the function on each node is smooth with Lipschitz gradient."},"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":"1807.00110","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-06-30T02:19:22Z","cross_cats_sorted":[],"title_canon_sha256":"33015c9b3891878cf9b51d529d46d0cb64872fb944da275c759df509ff39b58e","abstract_canon_sha256":"9e9f84f819415a291f18433cde722c8ca992bcb3f56d69fd963ef412bf43fed5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:32.364278Z","signature_b64":"GGzIsGu5wrohMmjzYb1vNTlDuVQvR7G6dzLsNgh/vgj7tFWUpQ8VcoiDIi6y9hEWiJXrMdu0ocv/og0Seau2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bab07ebecea47bce418d54e6b68e00d56793a87d1eaba63dedced9cb7cc86aca","last_reissued_at":"2026-05-18T00:07:32.363586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:32.363586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Linear and sublinear convergence rates for a subdifferentiable distributed deterministic asynchronous Dykstra's algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"C.H. Jeffrey Pang","submitted_at":"2018-06-30T02:19:22Z","abstract_excerpt":"In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra's algorithm, or block coordinate dual ascent. Each node in the distributed optimization problem is the sum of a known regularizing quadratic and a function to be minimized. In this paper, we prove sublinear convergence rates for the general algorithm, and a linear rate of convergence if the function on each node is smooth with Lipschitz gradient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00110","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.00110","created_at":"2026-05-18T00:07:32.363699+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.00110v2","created_at":"2026-05-18T00:07:32.363699+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00110","created_at":"2026-05-18T00:07:32.363699+00:00"},{"alias_kind":"pith_short_12","alias_value":"XKYH5PWOUR54","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XKYH5PWOUR544QMN","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XKYH5PWO","created_at":"2026-05-18T12:33:01.666342+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/XKYH5PWOUR544QMNKTTLNDQA2V","json":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V.json","graph_json":"https://pith.science/api/pith-number/XKYH5PWOUR544QMNKTTLNDQA2V/graph.json","events_json":"https://pith.science/api/pith-number/XKYH5PWOUR544QMNKTTLNDQA2V/events.json","paper":"https://pith.science/paper/XKYH5PWO"},"agent_actions":{"view_html":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V","download_json":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V.json","view_paper":"https://pith.science/paper/XKYH5PWO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.00110&json=true","fetch_graph":"https://pith.science/api/pith-number/XKYH5PWOUR544QMNKTTLNDQA2V/graph.json","fetch_events":"https://pith.science/api/pith-number/XKYH5PWOUR544QMNKTTLNDQA2V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V/action/storage_attestation","attest_author":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V/action/author_attestation","sign_citation":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V/action/citation_signature","submit_replication":"https://pith.science/pith/XKYH5PWOUR544QMNKTTLNDQA2V/action/replication_record"}},"created_at":"2026-05-18T00:07:32.363699+00:00","updated_at":"2026-05-18T00:07:32.363699+00:00"}