{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MQVV5VTN4EJC5ZVSDW5L4ISRLW","short_pith_number":"pith:MQVV5VTN","schema_version":"1.0","canonical_sha256":"642b5ed66de1122ee6b21dbabe22515db35a499262a4aaf2aa01a7d3442b3364","source":{"kind":"arxiv","id":"1708.07164","version":4},"attestation_state":"computed","paper":{"title":"Newton-Type Methods for Non-Convex Optimization Under Inexact Hessian Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Fred Roosta, Michael W. Mahoney, Peng Xu","submitted_at":"2017-08-23T19:40:55Z","abstract_excerpt":"We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve $ \\epsilon $-approximate second-order optimality which have shown to be tight. Our Hessian approximation conditions constitute a major relaxation over the existing ones in the literature. Consequently, we are able to show that such mild conditions allow for the construction of the approximate Hessian"},"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":"1708.07164","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-08-23T19:40:55Z","cross_cats_sorted":["cs.CC","cs.LG","stat.ML"],"title_canon_sha256":"3b7ffe2b2c7c5b78810644eca630da160e143cd5474b964dc7d3d164025803b2","abstract_canon_sha256":"7a141ca1e6e51c2d8ed539a61d5d506c8f3f57036203e741d78ac75d012a33a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:22.084702Z","signature_b64":"DXk5Y3fchp4Fy6hGwokMIgazN66MrBtHnh2RebMF540fOfxTXnfPVBF6v0jyDO8UHl9lFIxLA7ys+bpmUbqaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"642b5ed66de1122ee6b21dbabe22515db35a499262a4aaf2aa01a7d3442b3364","last_reissued_at":"2026-05-17T23:46:22.084165Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:22.084165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Newton-Type Methods for Non-Convex Optimization Under Inexact Hessian Information","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.LG","stat.ML"],"primary_cat":"math.OC","authors_text":"Fred Roosta, Michael W. Mahoney, Peng Xu","submitted_at":"2017-08-23T19:40:55Z","abstract_excerpt":"We consider variants of trust-region and cubic regularization methods for non-convex optimization, in which the Hessian matrix is approximated. Under mild conditions on the inexact Hessian, and using approximate solution of the corresponding sub-problems, we provide iteration complexity to achieve $ \\epsilon $-approximate second-order optimality which have shown to be tight. Our Hessian approximation conditions constitute a major relaxation over the existing ones in the literature. Consequently, we are able to show that such mild conditions allow for the construction of the approximate Hessian"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07164","kind":"arxiv","version":4},"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":"1708.07164","created_at":"2026-05-17T23:46:22.084251+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.07164v4","created_at":"2026-05-17T23:46:22.084251+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07164","created_at":"2026-05-17T23:46:22.084251+00:00"},{"alias_kind":"pith_short_12","alias_value":"MQVV5VTN4EJC","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MQVV5VTN4EJC5ZVS","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MQVV5VTN","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/MQVV5VTN4EJC5ZVSDW5L4ISRLW","json":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW.json","graph_json":"https://pith.science/api/pith-number/MQVV5VTN4EJC5ZVSDW5L4ISRLW/graph.json","events_json":"https://pith.science/api/pith-number/MQVV5VTN4EJC5ZVSDW5L4ISRLW/events.json","paper":"https://pith.science/paper/MQVV5VTN"},"agent_actions":{"view_html":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW","download_json":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW.json","view_paper":"https://pith.science/paper/MQVV5VTN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.07164&json=true","fetch_graph":"https://pith.science/api/pith-number/MQVV5VTN4EJC5ZVSDW5L4ISRLW/graph.json","fetch_events":"https://pith.science/api/pith-number/MQVV5VTN4EJC5ZVSDW5L4ISRLW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW/action/storage_attestation","attest_author":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW/action/author_attestation","sign_citation":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW/action/citation_signature","submit_replication":"https://pith.science/pith/MQVV5VTN4EJC5ZVSDW5L4ISRLW/action/replication_record"}},"created_at":"2026-05-17T23:46:22.084251+00:00","updated_at":"2026-05-17T23:46:22.084251+00:00"}