{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NLRHVVQTJKYFJFLOADT3HQZZOB","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":"ab2d05eb6ba73e35834a4c4e2e074d0e753da360a6954868ed8f7bf4c5960759","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-27T23:04:31Z","title_canon_sha256":"d3fab6dbd3f255829f80283154981ffaf4fcecbdd4cd220f0148c169369b076e"},"schema_version":"1.0","source":{"id":"1109.6058","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6058","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6058v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6058","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"NLRHVVQTJKYF","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NLRHVVQTJKYFJFLO","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NLRHVVQT","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:36dabceb233337ff5c678a66d3b36a9b1d8eff27012446cf2b9f4c565cf6c38b","target":"graph","created_at":"2026-05-18T04:12:09Z","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":"We modify Nesterov's constant step gradient method for strongly convex functions with Lipschitz continuous gradient described in Nesterov's book. Nesterov shows that $f(x_k) - f^* \\leq L \\prod_{i=1}^k (1 - \\alpha_k) \\| x_0 - x^* \\|_2^2$ with $\\alpha_k = \\sqrt{\\rho}$ for all $k$, where $L$ is the Lipschitz gradient constant and $\\rho$ is the reciprocal condition number of $f(x)$. Hence the convergence rate is $1-\\sqrt{\\rho}$. In this work, we try to accelerate Nesterov's method by adaptively searching for an $\\alpha_k > \\sqrt{\\rho}$ at each iteration. The proposed method evaluates the gradient ","authors_text":"Hao Chen, Xiangrui Meng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-27T23:04:31Z","title":"Accelerating Nesterov's Method for Strongly Convex Functions with Lipschitz Gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6058","kind":"arxiv","version":1},"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":"sha256:1e72a7930be90a1b60c4827b917d9002e0129249cbaf3ba8a08affd42e67c5e4","target":"record","created_at":"2026-05-18T04:12:09Z","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":"ab2d05eb6ba73e35834a4c4e2e074d0e753da360a6954868ed8f7bf4c5960759","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-27T23:04:31Z","title_canon_sha256":"d3fab6dbd3f255829f80283154981ffaf4fcecbdd4cd220f0148c169369b076e"},"schema_version":"1.0","source":{"id":"1109.6058","kind":"arxiv","version":1}},"canonical_sha256":"6ae27ad6134ab054956e00e7b3c339704d1af796917fd0326e677f6034f15615","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ae27ad6134ab054956e00e7b3c339704d1af796917fd0326e677f6034f15615","first_computed_at":"2026-05-18T04:12:09.832936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:09.832936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yq2McTKsxY9YVSKavQRp1mADYwsiQ3c+WcA0fm4MQawWYFIrjxDGNrpmyypZknJfqsaLDiGMcF885l64Mm87AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:09.833407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6058","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e72a7930be90a1b60c4827b917d9002e0129249cbaf3ba8a08affd42e67c5e4","sha256:36dabceb233337ff5c678a66d3b36a9b1d8eff27012446cf2b9f4c565cf6c38b"],"state_sha256":"1fd39d80aafa84ec39349bdbf2fd3aec3ae06abe4cec325a72195f4c999cd526"}