{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:WJ62E63MB3T5JVP7MWBNHTLE2R","short_pith_number":"pith:WJ62E63M","schema_version":"1.0","canonical_sha256":"b27da27b6c0ee7d4d5ff6582d3cd64d45cb114a82fa44cfc4fee4fe7b9435b52","source":{"kind":"arxiv","id":"1710.11307","version":2},"attestation_state":"computed","paper":{"title":"Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Narin Petrot, Nimit Nimana","submitted_at":"2017-10-31T03:08:55Z","abstract_excerpt":"We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximal monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided the condition corresponded to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong conve"},"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":"1710.11307","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-10-31T03:08:55Z","cross_cats_sorted":[],"title_canon_sha256":"1f4bdf937e2b734afb956b43ceb5699776708e475ad73ceb4cc291c694b6fb15","abstract_canon_sha256":"2f6927aaea840b7c0a91fcc4db86ed0eed433a89bc7e563042d33e70d9368d2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:36.358194Z","signature_b64":"0xMf3CKV90gHrVQGwUjsSmO7n+rTh+cgalLzjU7nso/z/u+KMvkfxZaoWSTuHH/Ia40j3bqdYPP6oR0tayDMBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27da27b6c0ee7d4d5ff6582d3cd64d45cb114a82fa44cfc4fee4fe7b9435b52","last_reissued_at":"2026-05-18T00:09:36.357742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:36.357742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Forward-Backward Splitting with Penalization for Monotone Inclusion Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Narin Petrot, Nimit Nimana","submitted_at":"2017-10-31T03:08:55Z","abstract_excerpt":"We introduce a generalized forward-backward splitting method with penalty term for solving monotone inclusion problems involving the sum of a finite number of maximally monotone operators and the normal cone to the nonempty set of zeros of another maximal monotone operator. We show weak ergodic convergence of the generated sequence of iterates to a solution of the considered monotone inclusion problem, provided the condition corresponded to the Fitzpatrick function of the operator describing the set of the normal cone is fulfilled. Under strong monotonicity of an operator, we show strong conve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11307","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":"1710.11307","created_at":"2026-05-18T00:09:36.357805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.11307v2","created_at":"2026-05-18T00:09:36.357805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11307","created_at":"2026-05-18T00:09:36.357805+00:00"},{"alias_kind":"pith_short_12","alias_value":"WJ62E63MB3T5","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_16","alias_value":"WJ62E63MB3T5JVP7","created_at":"2026-05-18T12:31:53.515858+00:00"},{"alias_kind":"pith_short_8","alias_value":"WJ62E63M","created_at":"2026-05-18T12:31:53.515858+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/WJ62E63MB3T5JVP7MWBNHTLE2R","json":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R.json","graph_json":"https://pith.science/api/pith-number/WJ62E63MB3T5JVP7MWBNHTLE2R/graph.json","events_json":"https://pith.science/api/pith-number/WJ62E63MB3T5JVP7MWBNHTLE2R/events.json","paper":"https://pith.science/paper/WJ62E63M"},"agent_actions":{"view_html":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R","download_json":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R.json","view_paper":"https://pith.science/paper/WJ62E63M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.11307&json=true","fetch_graph":"https://pith.science/api/pith-number/WJ62E63MB3T5JVP7MWBNHTLE2R/graph.json","fetch_events":"https://pith.science/api/pith-number/WJ62E63MB3T5JVP7MWBNHTLE2R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R/action/storage_attestation","attest_author":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R/action/author_attestation","sign_citation":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R/action/citation_signature","submit_replication":"https://pith.science/pith/WJ62E63MB3T5JVP7MWBNHTLE2R/action/replication_record"}},"created_at":"2026-05-18T00:09:36.357805+00:00","updated_at":"2026-05-18T00:09:36.357805+00:00"}