{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:PYCDCQOSUZ7MLJ3CDWOTNGMW7Y","short_pith_number":"pith:PYCDCQOS","schema_version":"1.0","canonical_sha256":"7e043141d2a67ec5a7621d9d369996fe1c7e40ad28cab7c730df89669a08fa5d","source":{"kind":"arxiv","id":"0804.3835","version":5},"attestation_state":"computed","paper":{"title":"A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Jin Yu, Nicol N. Schraudolph, Simon Guenter, S.V.N. Vishwanathan","submitted_at":"2008-04-24T04:38:54Z","abstract_excerpt":"We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the local quadratic model, the identification of a descent direction, and the Wolfe line search conditions. We prove that under some technical conditions, the resulting subBFGS algorithm is globally convergent in objective function value. We apply its memory-limited variant (subLBFGS) to L_2-regularized risk minimization with the binary hinge loss. To extend our"},"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":"0804.3835","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-04-24T04:38:54Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"beaaebe2a9348a622e633d8bb7f3007bcc71c210511b7896045d1083313d0742","abstract_canon_sha256":"55c0e471011def2c3862052b55770e21034679b6f669ca2683dab803be816e69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:38.246360Z","signature_b64":"P95wGdfF1K5Kyiy8HDWlud1MevJ5+ynDtEsiI/6D5vTQduR61P20Rs8o2KsWn4ZDuJRTlpC0U6AF9vjVufSkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e043141d2a67ec5a7621d9d369996fe1c7e40ad28cab7c730df89669a08fa5d","last_reissued_at":"2026-05-18T04:34:38.245628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:38.245628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Quasi-Newton Approach to Nonsmooth Convex Optimization Problems in Machine Learning","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"stat.ML","authors_text":"Jin Yu, Nicol N. Schraudolph, Simon Guenter, S.V.N. Vishwanathan","submitted_at":"2008-04-24T04:38:54Z","abstract_excerpt":"We extend the well-known BFGS quasi-Newton method and its memory-limited variant LBFGS to the optimization of nonsmooth convex objectives. This is done in a rigorous fashion by generalizing three components of BFGS to subdifferentials: the local quadratic model, the identification of a descent direction, and the Wolfe line search conditions. We prove that under some technical conditions, the resulting subBFGS algorithm is globally convergent in objective function value. We apply its memory-limited variant (subLBFGS) to L_2-regularized risk minimization with the binary hinge loss. To extend our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3835","kind":"arxiv","version":5},"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":"0804.3835","created_at":"2026-05-18T04:34:38.245725+00:00"},{"alias_kind":"arxiv_version","alias_value":"0804.3835v5","created_at":"2026-05-18T04:34:38.245725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.3835","created_at":"2026-05-18T04:34:38.245725+00:00"},{"alias_kind":"pith_short_12","alias_value":"PYCDCQOSUZ7M","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"PYCDCQOSUZ7MLJ3C","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"PYCDCQOS","created_at":"2026-05-18T12:25:57.157939+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/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y","json":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y.json","graph_json":"https://pith.science/api/pith-number/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/graph.json","events_json":"https://pith.science/api/pith-number/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/events.json","paper":"https://pith.science/paper/PYCDCQOS"},"agent_actions":{"view_html":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y","download_json":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y.json","view_paper":"https://pith.science/paper/PYCDCQOS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0804.3835&json=true","fetch_graph":"https://pith.science/api/pith-number/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/graph.json","fetch_events":"https://pith.science/api/pith-number/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/action/storage_attestation","attest_author":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/action/author_attestation","sign_citation":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/action/citation_signature","submit_replication":"https://pith.science/pith/PYCDCQOSUZ7MLJ3CDWOTNGMW7Y/action/replication_record"}},"created_at":"2026-05-18T04:34:38.245725+00:00","updated_at":"2026-05-18T04:34:38.245725+00:00"}