{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IAYPJFVUGHCG2QFLSUSOJJRESE","short_pith_number":"pith:IAYPJFVU","schema_version":"1.0","canonical_sha256":"4030f496b431c46d40ab9524e4a62491283eab1921789d4ad63ef914270aca63","source":{"kind":"arxiv","id":"1509.09257","version":2},"attestation_state":"computed","paper":{"title":"Incremental Aggregated Proximal and Augmented Lagrangian Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Dimitri P. Bertsekas","submitted_at":"2015-09-30T17:12:09Z","abstract_excerpt":"We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods that have received a lot of recent attention. Under cost function differentiability and strong convexity assumptions, we show linear convergence for a sufficiently small constant stepsize. This result also applies to distributed asynchronous variants of the method, involving bounded interprocessor communication delays.\n  We then consider dual versions of increm"},"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":"1509.09257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2015-09-30T17:12:09Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4534db0994a3674e2092cece6c62020957a8f182bbdd8c63fa3c790eb8021e7d","abstract_canon_sha256":"75f71b45e519365267f5881357dcc115439c4a94ea785942f2e861ffab33591f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:53.485688Z","signature_b64":"FUxb8bsdPH/7Q7G1b4V1w2j2WB58o85ol4QUVM2i2HKYlA03AAnizDaLjuIzEncrwom2MVamnItdj1mVZUDqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4030f496b431c46d40ab9524e4a62491283eab1921789d4ad63ef914270aca63","last_reissued_at":"2026-05-18T01:27:53.484991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:53.484991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Incremental Aggregated Proximal and Augmented Lagrangian Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.SY","authors_text":"Dimitri P. Bertsekas","submitted_at":"2015-09-30T17:12:09Z","abstract_excerpt":"We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods that have received a lot of recent attention. Under cost function differentiability and strong convexity assumptions, we show linear convergence for a sufficiently small constant stepsize. This result also applies to distributed asynchronous variants of the method, involving bounded interprocessor communication delays.\n  We then consider dual versions of increm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09257","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":"1509.09257","created_at":"2026-05-18T01:27:53.485090+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.09257v2","created_at":"2026-05-18T01:27:53.485090+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09257","created_at":"2026-05-18T01:27:53.485090+00:00"},{"alias_kind":"pith_short_12","alias_value":"IAYPJFVUGHCG","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IAYPJFVUGHCG2QFL","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IAYPJFVU","created_at":"2026-05-18T12:29:25.134429+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/IAYPJFVUGHCG2QFLSUSOJJRESE","json":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE.json","graph_json":"https://pith.science/api/pith-number/IAYPJFVUGHCG2QFLSUSOJJRESE/graph.json","events_json":"https://pith.science/api/pith-number/IAYPJFVUGHCG2QFLSUSOJJRESE/events.json","paper":"https://pith.science/paper/IAYPJFVU"},"agent_actions":{"view_html":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE","download_json":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE.json","view_paper":"https://pith.science/paper/IAYPJFVU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.09257&json=true","fetch_graph":"https://pith.science/api/pith-number/IAYPJFVUGHCG2QFLSUSOJJRESE/graph.json","fetch_events":"https://pith.science/api/pith-number/IAYPJFVUGHCG2QFLSUSOJJRESE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE/action/storage_attestation","attest_author":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE/action/author_attestation","sign_citation":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE/action/citation_signature","submit_replication":"https://pith.science/pith/IAYPJFVUGHCG2QFLSUSOJJRESE/action/replication_record"}},"created_at":"2026-05-18T01:27:53.485090+00:00","updated_at":"2026-05-18T01:27:53.485090+00:00"}