{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZJKV2AUPLZ7OKOL3NB634SOOVL","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":"c07c632980a0ed9b54f04865f430772164597a8dd91762e37bd2da8c1b02bce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-23T13:50:35Z","title_canon_sha256":"710a62aa7445bb63837f691e2587aeeeea5a6f114ebe41e03e429a470a0e9c91"},"schema_version":"1.0","source":{"id":"2404.15051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.15051","created_at":"2026-07-05T08:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"2404.15051v1","created_at":"2026-07-05T08:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.15051","created_at":"2026-07-05T08:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"ZJKV2AUPLZ7O","created_at":"2026-07-05T08:11:14Z"},{"alias_kind":"pith_short_16","alias_value":"ZJKV2AUPLZ7OKOL3","created_at":"2026-07-05T08:11:14Z"},{"alias_kind":"pith_short_8","alias_value":"ZJKV2AUP","created_at":"2026-07-05T08:11:14Z"}],"graph_snapshots":[{"event_id":"sha256:8f37a9431e75d901025f48e71e4bf96f3b0f4a1328cbf27895b4393672820736","target":"graph","created_at":"2026-07-05T08:11:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2404.15051/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a global complexity analysis of the classical BFGS method with inexact line search, as applied to minimizing a strongly convex function with Lipschitz continuous gradient and Hessian. We consider a variety of standard line search strategies including the backtracking line search based on the Armijo condition, Armijo-Goldstein and Wolfe-Powell line searches. Our analysis suggests that the convergence of the algorithm proceeds in several different stages before the fast superlinear convergence actually begins. Furthermore, once the initial point is far away from the min","authors_text":"Anton Rodomanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-23T13:50:35Z","title":"Global Complexity Analysis of BFGS"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.15051","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":"sha256:70bf8a5781c0f07c90c9c4780b0af79cacd49f1318b5dec7c284a313e9cf312a","target":"record","created_at":"2026-07-05T08:11:14Z","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":"c07c632980a0ed9b54f04865f430772164597a8dd91762e37bd2da8c1b02bce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-04-23T13:50:35Z","title_canon_sha256":"710a62aa7445bb63837f691e2587aeeeea5a6f114ebe41e03e429a470a0e9c91"},"schema_version":"1.0","source":{"id":"2404.15051","kind":"arxiv","version":1}},"canonical_sha256":"ca555d028f5e7ee5397b687dbe49ceaae1157b761426fa45b3224a7fbddcf7ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca555d028f5e7ee5397b687dbe49ceaae1157b761426fa45b3224a7fbddcf7ff","first_computed_at":"2026-07-05T08:11:14.540414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:11:14.540414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mWzR6N3AF8yvn+JcIvZAAcGoGtvJ9pIbZxCsc6/Om8FzgC40bITTNhQ31GXiDJldFJNPqCtcB4eIlOC9BGZxCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:11:14.540842Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.15051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70bf8a5781c0f07c90c9c4780b0af79cacd49f1318b5dec7c284a313e9cf312a","sha256:8f37a9431e75d901025f48e71e4bf96f3b0f4a1328cbf27895b4393672820736"],"state_sha256":"1a31c1bc7e54b7a8c6174069b99e9cd93ff0fac93e54eafb8c610c3912345bd5"}