{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:P744DQFU62FOT7S6ZWBA5QM2BN","short_pith_number":"pith:P744DQFU","schema_version":"1.0","canonical_sha256":"7ff9c1c0b4f68ae9fe5ecd820ec19a0b70df5c81e79adc2ee7e04574f8643621","source":{"kind":"arxiv","id":"2504.15752","version":3},"attestation_state":"computed","paper":{"title":"On the complexity of proximal gradient and proximal gradient-Newton-CG methods for \\(\\ell_1\\)-regularized Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hong Zhu","submitted_at":"2025-04-22T09:56:28Z","abstract_excerpt":"In this paper, we propose two second-order methods for solving the \\(\\ell_1\\)-regularized composite optimization problem, which are developed based on two distinct definitions of approximate second-order stationary points. We introduce a hybrid proximal gradient and negative curvature method, as well as an adaptive hybrid proximal gradient-Newton-CG method with negative curvature directions, to find a strong* approximate second-order stationary point and a weak approximate second-order stationary point for \\(\\ell_1\\)-regularized optimization problems, respectively. Comprehensive analyses are p"},"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":"2504.15752","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T09:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"aa1e6adacbdb950ca0e555feb45978270a817a35f6b88f6a9eaa006bc31db402","abstract_canon_sha256":"5713829722ca86cc0957953b52c74e5d89922cc5bdac37769f0c75be2de1590e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:29.630532Z","signature_b64":"NQQ39RphvfMM8kHtzxsQgqpObvTKzHDiEWB1Mcgo0mZ3sIYosam4RIeLVCeMWGlerpxctT/WZhXXIJSLuK1TCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ff9c1c0b4f68ae9fe5ecd820ec19a0b70df5c81e79adc2ee7e04574f8643621","last_reissued_at":"2026-06-19T16:10:29.630099Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:29.630099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the complexity of proximal gradient and proximal gradient-Newton-CG methods for \\(\\ell_1\\)-regularized Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hong Zhu","submitted_at":"2025-04-22T09:56:28Z","abstract_excerpt":"In this paper, we propose two second-order methods for solving the \\(\\ell_1\\)-regularized composite optimization problem, which are developed based on two distinct definitions of approximate second-order stationary points. We introduce a hybrid proximal gradient and negative curvature method, as well as an adaptive hybrid proximal gradient-Newton-CG method with negative curvature directions, to find a strong* approximate second-order stationary point and a weak approximate second-order stationary point for \\(\\ell_1\\)-regularized optimization problems, respectively. Comprehensive analyses are p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15752","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.15752/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.15752","created_at":"2026-06-19T16:10:29.630156+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.15752v3","created_at":"2026-06-19T16:10:29.630156+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15752","created_at":"2026-06-19T16:10:29.630156+00:00"},{"alias_kind":"pith_short_12","alias_value":"P744DQFU62FO","created_at":"2026-06-19T16:10:29.630156+00:00"},{"alias_kind":"pith_short_16","alias_value":"P744DQFU62FOT7S6","created_at":"2026-06-19T16:10:29.630156+00:00"},{"alias_kind":"pith_short_8","alias_value":"P744DQFU","created_at":"2026-06-19T16:10:29.630156+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/P744DQFU62FOT7S6ZWBA5QM2BN","json":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN.json","graph_json":"https://pith.science/api/pith-number/P744DQFU62FOT7S6ZWBA5QM2BN/graph.json","events_json":"https://pith.science/api/pith-number/P744DQFU62FOT7S6ZWBA5QM2BN/events.json","paper":"https://pith.science/paper/P744DQFU"},"agent_actions":{"view_html":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN","download_json":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN.json","view_paper":"https://pith.science/paper/P744DQFU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.15752&json=true","fetch_graph":"https://pith.science/api/pith-number/P744DQFU62FOT7S6ZWBA5QM2BN/graph.json","fetch_events":"https://pith.science/api/pith-number/P744DQFU62FOT7S6ZWBA5QM2BN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN/action/storage_attestation","attest_author":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN/action/author_attestation","sign_citation":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN/action/citation_signature","submit_replication":"https://pith.science/pith/P744DQFU62FOT7S6ZWBA5QM2BN/action/replication_record"}},"created_at":"2026-06-19T16:10:29.630156+00:00","updated_at":"2026-06-19T16:10:29.630156+00:00"}