{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GJVVOERLIGE4T3FHCD3E27QQTV","short_pith_number":"pith:GJVVOERL","schema_version":"1.0","canonical_sha256":"326b57122b4189c9eca710f64d7e109d54fb002dd4d4a862ffec420b84c12628","source":{"kind":"arxiv","id":"1808.02901","version":1},"attestation_state":"computed","paper":{"title":"Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Yangyang Xu, Yuyuan Ouyang","submitted_at":"2018-08-08T18:04:13Z","abstract_excerpt":"On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many efforts would guarantee a solution of desired accuracy. In this paper, we pursue the opposite direction by deriving lower complexity bounds of first-order methods on large-scale SPPs. Our results apply to the methods whose iterates are in the linear span of past first-order information, as well as more general methods that produce their iterates in an arbitrar"},"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":"1808.02901","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-08T18:04:13Z","cross_cats_sorted":[],"title_canon_sha256":"25151ce4963869c425aed3150216aca1e2c5d607bf068e9efc13082fd87e796a","abstract_canon_sha256":"2ddffb7dbd4371488dc6280136b5a90966ab540799e60dc1f774006750378ae8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:30.697643Z","signature_b64":"rU9M/a1Sel2kMyRsPfcyB32QFDPx9QPWx3lMjKEOeCT3bdtFO+iyLN56dBXF2tkjw72I98ZcXxuO7+CVQmUABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"326b57122b4189c9eca710f64d7e109d54fb002dd4d4a862ffec420b84c12628","last_reissued_at":"2026-05-18T00:08:30.697228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:30.697228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lower complexity bounds of first-order methods for convex-concave bilinear saddle-point problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Yangyang Xu, Yuyuan Ouyang","submitted_at":"2018-08-08T18:04:13Z","abstract_excerpt":"On solving a convex-concave bilinear saddle-point problem (SPP), there have been many works studying the complexity results of first-order methods. These results are all about upper complexity bounds, which can determine at most how many efforts would guarantee a solution of desired accuracy. In this paper, we pursue the opposite direction by deriving lower complexity bounds of first-order methods on large-scale SPPs. Our results apply to the methods whose iterates are in the linear span of past first-order information, as well as more general methods that produce their iterates in an arbitrar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02901","kind":"arxiv","version":1},"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":"1808.02901","created_at":"2026-05-18T00:08:30.697295+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.02901v1","created_at":"2026-05-18T00:08:30.697295+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02901","created_at":"2026-05-18T00:08:30.697295+00:00"},{"alias_kind":"pith_short_12","alias_value":"GJVVOERLIGE4","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GJVVOERLIGE4T3FH","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GJVVOERL","created_at":"2026-05-18T12:32:25.280505+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/GJVVOERLIGE4T3FHCD3E27QQTV","json":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV.json","graph_json":"https://pith.science/api/pith-number/GJVVOERLIGE4T3FHCD3E27QQTV/graph.json","events_json":"https://pith.science/api/pith-number/GJVVOERLIGE4T3FHCD3E27QQTV/events.json","paper":"https://pith.science/paper/GJVVOERL"},"agent_actions":{"view_html":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV","download_json":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV.json","view_paper":"https://pith.science/paper/GJVVOERL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.02901&json=true","fetch_graph":"https://pith.science/api/pith-number/GJVVOERLIGE4T3FHCD3E27QQTV/graph.json","fetch_events":"https://pith.science/api/pith-number/GJVVOERLIGE4T3FHCD3E27QQTV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV/action/storage_attestation","attest_author":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV/action/author_attestation","sign_citation":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV/action/citation_signature","submit_replication":"https://pith.science/pith/GJVVOERLIGE4T3FHCD3E27QQTV/action/replication_record"}},"created_at":"2026-05-18T00:08:30.697295+00:00","updated_at":"2026-05-18T00:08:30.697295+00:00"}