{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:P744DQFU62FOT7S6ZWBA5QM2BN","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":"5713829722ca86cc0957953b52c74e5d89922cc5bdac37769f0c75be2de1590e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T09:56:28Z","title_canon_sha256":"aa1e6adacbdb950ca0e555feb45978270a817a35f6b88f6a9eaa006bc31db402"},"schema_version":"1.0","source":{"id":"2504.15752","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.15752","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2504.15752v3","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.15752","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"P744DQFU62FO","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"P744DQFU62FOT7S6","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"P744DQFU","created_at":"2026-06-19T16:10:29Z"}],"graph_snapshots":[{"event_id":"sha256:d586a45cd7bb406997fe907f001dcd932a76685d12996d2d5441115b1c296d70","target":"graph","created_at":"2026-06-19T16:10:29Z","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/2504.15752/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Hong Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T09:56:28Z","title":"On the complexity of proximal gradient and proximal gradient-Newton-CG methods for \\(\\ell_1\\)-regularized Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.15752","kind":"arxiv","version":3},"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":"sha256:33fc81ddf80ddefea16ccc2e476d69a72372b3458feaad9565e886358e7fac3d","target":"record","created_at":"2026-06-19T16:10:29Z","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":"5713829722ca86cc0957953b52c74e5d89922cc5bdac37769f0c75be2de1590e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2025-04-22T09:56:28Z","title_canon_sha256":"aa1e6adacbdb950ca0e555feb45978270a817a35f6b88f6a9eaa006bc31db402"},"schema_version":"1.0","source":{"id":"2504.15752","kind":"arxiv","version":3}},"canonical_sha256":"7ff9c1c0b4f68ae9fe5ecd820ec19a0b70df5c81e79adc2ee7e04574f8643621","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ff9c1c0b4f68ae9fe5ecd820ec19a0b70df5c81e79adc2ee7e04574f8643621","first_computed_at":"2026-06-19T16:10:29.630099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:29.630099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NQQ39RphvfMM8kHtzxsQgqpObvTKzHDiEWB1Mcgo0mZ3sIYosam4RIeLVCeMWGlerpxctT/WZhXXIJSLuK1TCw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:29.630532Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.15752","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33fc81ddf80ddefea16ccc2e476d69a72372b3458feaad9565e886358e7fac3d","sha256:d586a45cd7bb406997fe907f001dcd932a76685d12996d2d5441115b1c296d70"],"state_sha256":"854722f45a5449d9c0d2af291cb6a1084bacced3fdd22c915a3f3f66dfe8fa2f"}