{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:C6CGOY4YSK3L5QOLVEHE3DENNA","short_pith_number":"pith:C6CGOY4Y","schema_version":"1.0","canonical_sha256":"178467639892b6bec1cba90e4d8c8d6810307234f4abbb1a8916f5c32eae9ea1","source":{"kind":"arxiv","id":"1906.10053","version":3},"attestation_state":"computed","paper":{"title":"Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas Themelis, Panagiotis Patrinos, Puya Latafat","submitted_at":"2019-06-24T16:23:21Z","abstract_excerpt":"This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-\\L ojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting a"},"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":"1906.10053","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-24T16:23:21Z","cross_cats_sorted":[],"title_canon_sha256":"1423d6c3f3be40d6bc75d05b6edc4934b18f2508b5b7ee529ab17173c47d8a72","abstract_canon_sha256":"307c1c18be15ccdd5745d16dad110c284893891868d3dab803a7fa416c0ff94b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:08:14.284504Z","signature_b64":"TLoHAE2ODvTPCJJi5HY4LQnBJFgQakTW6YtXB4jrBxa46+7ZEo1oQfH8rtXV8XqCFc9vZ2KijFDc6XvfHHyPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"178467639892b6bec1cba90e4d8c8d6810307234f4abbb1a8916f5c32eae9ea1","last_reissued_at":"2026-07-05T08:08:14.284085Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:08:14.284085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Andreas Themelis, Panagiotis Patrinos, Puya Latafat","submitted_at":"2019-06-24T16:23:21Z","abstract_excerpt":"This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-\\L ojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10053","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.10053/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1906.10053","created_at":"2026-07-05T08:08:14.284140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.10053v3","created_at":"2026-07-05T08:08:14.284140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10053","created_at":"2026-07-05T08:08:14.284140+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6CGOY4YSK3L","created_at":"2026-07-05T08:08:14.284140+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6CGOY4YSK3L5QOL","created_at":"2026-07-05T08:08:14.284140+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6CGOY4Y","created_at":"2026-07-05T08:08:14.284140+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.01402","citing_title":"Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization","ref_index":39,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA","json":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA.json","graph_json":"https://pith.science/api/pith-number/C6CGOY4YSK3L5QOLVEHE3DENNA/graph.json","events_json":"https://pith.science/api/pith-number/C6CGOY4YSK3L5QOLVEHE3DENNA/events.json","paper":"https://pith.science/paper/C6CGOY4Y"},"agent_actions":{"view_html":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA","download_json":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA.json","view_paper":"https://pith.science/paper/C6CGOY4Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.10053&json=true","fetch_graph":"https://pith.science/api/pith-number/C6CGOY4YSK3L5QOLVEHE3DENNA/graph.json","fetch_events":"https://pith.science/api/pith-number/C6CGOY4YSK3L5QOLVEHE3DENNA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA/action/storage_attestation","attest_author":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA/action/author_attestation","sign_citation":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA/action/citation_signature","submit_replication":"https://pith.science/pith/C6CGOY4YSK3L5QOLVEHE3DENNA/action/replication_record"}},"created_at":"2026-07-05T08:08:14.284140+00:00","updated_at":"2026-07-05T08:08:14.284140+00:00"}