{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:K4TDUNHJOEWERVSGZQBUBV6ODW","short_pith_number":"pith:K4TDUNHJ","schema_version":"1.0","canonical_sha256":"57263a34e9712c48d646cc0340d7ce1d8d684c4266605abff4a8a33475f5f9e9","source":{"kind":"arxiv","id":"2009.01451","version":2},"attestation_state":"computed","paper":{"title":"Sufficient Descent Riemannian Conjugate Gradient Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hideaki Iiduka, Hiroyuki Sakai","submitted_at":"2020-09-03T05:07:52Z","abstract_excerpt":"This paper considers sufficient descent Riemannian conjugate gradient methods with line search algorithms. We propose two kinds of sufficient descent nonlinear conjugate gradient methods and prove these methods satisfy the sufficient descent condition even on Riemannian manifolds. One is the hybrid method combining the Fletcher-Reeves-type method with the Polak-Ribiere-Polyak-type method, and the other is the Hager-Zhang-type method, both of which are generalizations of those used in Euclidean space. Also, we generalize two kinds of line search algorithms that are widely used in Euclidean spac"},"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":"2009.01451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-03T05:07:52Z","cross_cats_sorted":[],"title_canon_sha256":"45cffcdcd07177b2f4df752590424a4c9ff819a7adb518d633a23dd058fd0d72","abstract_canon_sha256":"3d3f09e2145880bd8f06560cd8d3e4b4f51c1585fc6a9b12d4ab1e892f25d2e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:35:01.465984Z","signature_b64":"MFTz8iGsmjSy2lfrn8NzuQwJa9JUdEwR6LQ96doxCbB5SO+lQlD0EaG5J0O7sTu8fK7SbBc+WZcMDFwMqBoLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57263a34e9712c48d646cc0340d7ce1d8d684c4266605abff4a8a33475f5f9e9","last_reissued_at":"2026-07-05T02:35:01.465581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:35:01.465581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sufficient Descent Riemannian Conjugate Gradient Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hideaki Iiduka, Hiroyuki Sakai","submitted_at":"2020-09-03T05:07:52Z","abstract_excerpt":"This paper considers sufficient descent Riemannian conjugate gradient methods with line search algorithms. We propose two kinds of sufficient descent nonlinear conjugate gradient methods and prove these methods satisfy the sufficient descent condition even on Riemannian manifolds. One is the hybrid method combining the Fletcher-Reeves-type method with the Polak-Ribiere-Polyak-type method, and the other is the Hager-Zhang-type method, both of which are generalizations of those used in Euclidean space. Also, we generalize two kinds of line search algorithms that are widely used in Euclidean spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.01451","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2009.01451/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":"2009.01451","created_at":"2026-07-05T02:35:01.465636+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.01451v2","created_at":"2026-07-05T02:35:01.465636+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.01451","created_at":"2026-07-05T02:35:01.465636+00:00"},{"alias_kind":"pith_short_12","alias_value":"K4TDUNHJOEWE","created_at":"2026-07-05T02:35:01.465636+00:00"},{"alias_kind":"pith_short_16","alias_value":"K4TDUNHJOEWERVSG","created_at":"2026-07-05T02:35:01.465636+00:00"},{"alias_kind":"pith_short_8","alias_value":"K4TDUNHJ","created_at":"2026-07-05T02:35:01.465636+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/K4TDUNHJOEWERVSGZQBUBV6ODW","json":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW.json","graph_json":"https://pith.science/api/pith-number/K4TDUNHJOEWERVSGZQBUBV6ODW/graph.json","events_json":"https://pith.science/api/pith-number/K4TDUNHJOEWERVSGZQBUBV6ODW/events.json","paper":"https://pith.science/paper/K4TDUNHJ"},"agent_actions":{"view_html":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW","download_json":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW.json","view_paper":"https://pith.science/paper/K4TDUNHJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.01451&json=true","fetch_graph":"https://pith.science/api/pith-number/K4TDUNHJOEWERVSGZQBUBV6ODW/graph.json","fetch_events":"https://pith.science/api/pith-number/K4TDUNHJOEWERVSGZQBUBV6ODW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW/action/storage_attestation","attest_author":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW/action/author_attestation","sign_citation":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW/action/citation_signature","submit_replication":"https://pith.science/pith/K4TDUNHJOEWERVSGZQBUBV6ODW/action/replication_record"}},"created_at":"2026-07-05T02:35:01.465636+00:00","updated_at":"2026-07-05T02:35:01.465636+00:00"}