{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MVO6VOQEHZ6EWRWJNJLLEDX2UF","short_pith_number":"pith:MVO6VOQE","schema_version":"1.0","canonical_sha256":"655deaba043e7c4b46c96a56b20efaa16321ccda3c5087c5408ff4bb04d7be69","source":{"kind":"arxiv","id":"1712.09498","version":2},"attestation_state":"computed","paper":{"title":"A single potential governing convergence of conjugate gradient, accelerated gradient and geometric descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sahar Karimi, Stephen Vavasis","submitted_at":"2017-12-27T05:26:36Z","abstract_excerpt":"Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly convex function $f$ is known to reduce $f({\\bf x}_k)-f({\\bf x}^*)$ by a factor of $\\epsilon\\in(0,1)$ after $k=O(\\sqrt{L/\\ell}\\log(1/\\epsilon))$ iterations, where $\\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the function-gradient oracle model of computation. Modulo a line search, the geometric descent (GD) method of Bubeck, Lee and Singh has the same bound for this class of functions. The method of linear conjugate gradients (CG) also "},"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":"1712.09498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-12-27T05:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"b8507a7c49b08c0e1025028ffa5d02bd523e0965da528f9038f3b8ffb81178fa","abstract_canon_sha256":"152756ba790e2e6e9716fbf55b750ad5eb1f3488de5f0b2c0c78f62b1abbade2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:38.864866Z","signature_b64":"5rACg8hG5PlDsjuRxqwZxVbUlROgsbK34qEtZQqEeDVmIZkA1CvXwj7V6qRfiSXGOsZlmmo3IPtiuUkmzUTpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"655deaba043e7c4b46c96a56b20efaa16321ccda3c5087c5408ff4bb04d7be69","last_reissued_at":"2026-05-17T23:56:38.864195Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:38.864195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A single potential governing convergence of conjugate gradient, accelerated gradient and geometric descent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Sahar Karimi, Stephen Vavasis","submitted_at":"2017-12-27T05:26:36Z","abstract_excerpt":"Nesterov's accelerated gradient (AG) method for minimizing a smooth strongly convex function $f$ is known to reduce $f({\\bf x}_k)-f({\\bf x}^*)$ by a factor of $\\epsilon\\in(0,1)$ after $k=O(\\sqrt{L/\\ell}\\log(1/\\epsilon))$ iterations, where $\\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the function-gradient oracle model of computation. Modulo a line search, the geometric descent (GD) method of Bubeck, Lee and Singh has the same bound for this class of functions. The method of linear conjugate gradients (CG) also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09498","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":"1712.09498","created_at":"2026-05-17T23:56:38.864300+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09498v2","created_at":"2026-05-17T23:56:38.864300+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09498","created_at":"2026-05-17T23:56:38.864300+00:00"},{"alias_kind":"pith_short_12","alias_value":"MVO6VOQEHZ6E","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MVO6VOQEHZ6EWRWJ","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MVO6VOQE","created_at":"2026-05-18T12:31:31.346846+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/MVO6VOQEHZ6EWRWJNJLLEDX2UF","json":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF.json","graph_json":"https://pith.science/api/pith-number/MVO6VOQEHZ6EWRWJNJLLEDX2UF/graph.json","events_json":"https://pith.science/api/pith-number/MVO6VOQEHZ6EWRWJNJLLEDX2UF/events.json","paper":"https://pith.science/paper/MVO6VOQE"},"agent_actions":{"view_html":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF","download_json":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF.json","view_paper":"https://pith.science/paper/MVO6VOQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09498&json=true","fetch_graph":"https://pith.science/api/pith-number/MVO6VOQEHZ6EWRWJNJLLEDX2UF/graph.json","fetch_events":"https://pith.science/api/pith-number/MVO6VOQEHZ6EWRWJNJLLEDX2UF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF/action/storage_attestation","attest_author":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF/action/author_attestation","sign_citation":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF/action/citation_signature","submit_replication":"https://pith.science/pith/MVO6VOQEHZ6EWRWJNJLLEDX2UF/action/replication_record"}},"created_at":"2026-05-17T23:56:38.864300+00:00","updated_at":"2026-05-17T23:56:38.864300+00:00"}