{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7PV47V44NFY6JDL4TWA446NQUL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"19b9fa60e23fe2ab3ac8a520e2c1cea7b924b2cac4192f5366f5a9c87287d59a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2014-02-24T16:54:01Z","title_canon_sha256":"aacb4c0ac801c5ad78d57f3597ecdc8fedb4404110bce05e266d645933693945"},"schema_version":"1.0","source":{"id":"1402.5884","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.5884","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"arxiv_version","alias_value":"1402.5884v3","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.5884","created_at":"2026-05-18T01:35:40Z"},{"alias_kind":"pith_short_12","alias_value":"7PV47V44NFY6","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7PV47V44NFY6JDL4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7PV47V44","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:61ec91ada6cd45855d9fe996b5569a56424295d1d0ede3acd2d60192043c239f","target":"graph","created_at":"2026-05-18T01:35:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This work focuses on convergence analysis of the projected gradient method for solving constrained convex minimization problem in Hilbert spaces. We show that the sequence of points generated by the method employing the Armijo linesearch converges weakly to a solution of the considered convex optimization problem. Weak convergence is established by assuming convexity and Gateaux differentiability of the objective function, whose Gateaux derivative is supposed to be uniformly continuous on bounded sets. Furthermore, we propose some modifications in the classical projected gradient method in ord","authors_text":"Jose Yunier Bello Cruz, Welington de Oliveira","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2014-02-24T16:54:01Z","title":"On Weak and Strong Convergence of the Projected Gradient Method for Convex Optimization in real Hilbert Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5884","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8771ede69cd165397d34c7aa94fe91d5b920d99d653d909267c1ae4f23bc284c","target":"record","created_at":"2026-05-18T01:35:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"19b9fa60e23fe2ab3ac8a520e2c1cea7b924b2cac4192f5366f5a9c87287d59a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.OC","submitted_at":"2014-02-24T16:54:01Z","title_canon_sha256":"aacb4c0ac801c5ad78d57f3597ecdc8fedb4404110bce05e266d645933693945"},"schema_version":"1.0","source":{"id":"1402.5884","kind":"arxiv","version":3}},"canonical_sha256":"fbebcfd79c6971e48d7c9d81ce79b0a2d24bcc81e4e03071577680c6c2905591","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fbebcfd79c6971e48d7c9d81ce79b0a2d24bcc81e4e03071577680c6c2905591","first_computed_at":"2026-05-18T01:35:40.438642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:40.438642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HYDP46XbCZtb6q+3PTvO+9xtOC0c72bpd1LGK1lfSWU5uWhit0lJ0yyVAIv7khIrdABXaERnlmzbn//LW9cnBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:40.439382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.5884","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8771ede69cd165397d34c7aa94fe91d5b920d99d653d909267c1ae4f23bc284c","sha256:61ec91ada6cd45855d9fe996b5569a56424295d1d0ede3acd2d60192043c239f"],"state_sha256":"3d60e8679fa2581603ad90946d18ca3d126119ffc20bcd95c23f52fbc50966ba"}