{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:AUQNMBEIL3VIPH4AUDG4IFFAVS","short_pith_number":"pith:AUQNMBEI","schema_version":"1.0","canonical_sha256":"0520d604885eea879f80a0cdc414a0ac92d8dc703cebf47fbb400bb3ad101214","source":{"kind":"arxiv","id":"1405.4371","version":3},"attestation_state":"computed","paper":{"title":"A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hiroyuki Sato","submitted_at":"2014-05-17T08:55:51Z","abstract_excerpt":"This article describes a new Riemannian conjugate gradient method and presents a global convergence analysis. The existing Fletcher-Reeves-type Riemannian conjugate gradient method is guaranteed to be globally convergent if it is implemented with the strong Wolfe conditions. On the other hand, the Dai-Yuan-type Euclidean conjugate gradient method generates globally convergent sequences under the weak Wolfe conditions. This article deals with a generalization of Dai-Yuan's Euclidean algorithm to a Riemannian algorithm that requires only the weak Wolfe conditions. The global convergence property"},"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":"1405.4371","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-05-17T08:55:51Z","cross_cats_sorted":[],"title_canon_sha256":"91cf8705d1a9d0a87f2e5f653cd5cad47e98e1182e9caad4f956e7f427d53723","abstract_canon_sha256":"3c24d2ac90d03ce47926a79bc6808dd7ca8be107e9272dcb617587a8e56e89f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:20.109840Z","signature_b64":"cP3kXrLbT+bs+f58ouiaNNUtYKkNAJAfCQtZ31AC/NWsbUHWJrq8b0DwcYVR5PMlY+x/ji18irDGS/Z7iuv4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0520d604885eea879f80a0cdc414a0ac92d8dc703cebf47fbb400bb3ad101214","last_reissued_at":"2026-05-18T01:12:20.109468Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:20.109468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hiroyuki Sato","submitted_at":"2014-05-17T08:55:51Z","abstract_excerpt":"This article describes a new Riemannian conjugate gradient method and presents a global convergence analysis. The existing Fletcher-Reeves-type Riemannian conjugate gradient method is guaranteed to be globally convergent if it is implemented with the strong Wolfe conditions. On the other hand, the Dai-Yuan-type Euclidean conjugate gradient method generates globally convergent sequences under the weak Wolfe conditions. This article deals with a generalization of Dai-Yuan's Euclidean algorithm to a Riemannian algorithm that requires only the weak Wolfe conditions. The global convergence property"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4371","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":""},"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":"1405.4371","created_at":"2026-05-18T01:12:20.109523+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.4371v3","created_at":"2026-05-18T01:12:20.109523+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4371","created_at":"2026-05-18T01:12:20.109523+00:00"},{"alias_kind":"pith_short_12","alias_value":"AUQNMBEIL3VI","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AUQNMBEIL3VIPH4A","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AUQNMBEI","created_at":"2026-05-18T12:28:19.803747+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/AUQNMBEIL3VIPH4AUDG4IFFAVS","json":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS.json","graph_json":"https://pith.science/api/pith-number/AUQNMBEIL3VIPH4AUDG4IFFAVS/graph.json","events_json":"https://pith.science/api/pith-number/AUQNMBEIL3VIPH4AUDG4IFFAVS/events.json","paper":"https://pith.science/paper/AUQNMBEI"},"agent_actions":{"view_html":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS","download_json":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS.json","view_paper":"https://pith.science/paper/AUQNMBEI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.4371&json=true","fetch_graph":"https://pith.science/api/pith-number/AUQNMBEIL3VIPH4AUDG4IFFAVS/graph.json","fetch_events":"https://pith.science/api/pith-number/AUQNMBEIL3VIPH4AUDG4IFFAVS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS/action/storage_attestation","attest_author":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS/action/author_attestation","sign_citation":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS/action/citation_signature","submit_replication":"https://pith.science/pith/AUQNMBEIL3VIPH4AUDG4IFFAVS/action/replication_record"}},"created_at":"2026-05-18T01:12:20.109523+00:00","updated_at":"2026-05-18T01:12:20.109523+00:00"}