{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:VXNLVBZOFRWACOVRX5KQM3CZIV","short_pith_number":"pith:VXNLVBZO","schema_version":"1.0","canonical_sha256":"addaba872e2c6c013ab1bf55066c5945638173a45cd3bcc13597ae08d2921d2a","source":{"kind":"arxiv","id":"2007.12219","version":1},"attestation_state":"computed","paper":{"title":"A First-Order Primal-Dual Method for Nonconvex Constrained Optimization Based On the Augmented Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daoli Zhu, Lei Zhao, Shuzhong Zhang","submitted_at":"2020-07-23T19:16:13Z","abstract_excerpt":"Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on the augmented Lagrangian function we introduce a flexible first-order primal-dual method, to be called nonconvex auxiliary problem principle of augmented Lagrangian (NAPP-AL), for solving a class of nonlinearly constrained nonconvex and nonsmooth optimization problems. We demonstrate that NAPP-AL converges to a stationary solution at the rate of o(1/\\sqrt{k}), where k is the number of iterations. Moreover, under an a"},"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":"2007.12219","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-07-23T19:16:13Z","cross_cats_sorted":[],"title_canon_sha256":"6333c5f90465e5dc6b3ea64dcb6ea9655716f61755b4408d40b83fb61f90482f","abstract_canon_sha256":"d3c94b5c80027c3caec202b92a330a48bf00b845669da44b5c77419aec5c0dd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:21:50.343865Z","signature_b64":"inTFjksWe2rYXkflK2kvtozrjZhD0Lt8w+xIwEUG1IHuowxbbzuHchpWAmjgowNlzpOvr6y7H9Gsk0bt22B2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"addaba872e2c6c013ab1bf55066c5945638173a45cd3bcc13597ae08d2921d2a","last_reissued_at":"2026-07-05T01:21:50.343402Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:21:50.343402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A First-Order Primal-Dual Method for Nonconvex Constrained Optimization Based On the Augmented Lagrangian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Daoli Zhu, Lei Zhao, Shuzhong Zhang","submitted_at":"2020-07-23T19:16:13Z","abstract_excerpt":"Nonlinearly constrained nonconvex and nonsmooth optimization models play an increasingly important role in machine learning, statistics and data analytics. In this paper, based on the augmented Lagrangian function we introduce a flexible first-order primal-dual method, to be called nonconvex auxiliary problem principle of augmented Lagrangian (NAPP-AL), for solving a class of nonlinearly constrained nonconvex and nonsmooth optimization problems. We demonstrate that NAPP-AL converges to a stationary solution at the rate of o(1/\\sqrt{k}), where k is the number of iterations. Moreover, under an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.12219","kind":"arxiv","version":1},"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/2007.12219/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":"2007.12219","created_at":"2026-07-05T01:21:50.343459+00:00"},{"alias_kind":"arxiv_version","alias_value":"2007.12219v1","created_at":"2026-07-05T01:21:50.343459+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.12219","created_at":"2026-07-05T01:21:50.343459+00:00"},{"alias_kind":"pith_short_12","alias_value":"VXNLVBZOFRWA","created_at":"2026-07-05T01:21:50.343459+00:00"},{"alias_kind":"pith_short_16","alias_value":"VXNLVBZOFRWACOVR","created_at":"2026-07-05T01:21:50.343459+00:00"},{"alias_kind":"pith_short_8","alias_value":"VXNLVBZO","created_at":"2026-07-05T01:21:50.343459+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/VXNLVBZOFRWACOVRX5KQM3CZIV","json":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV.json","graph_json":"https://pith.science/api/pith-number/VXNLVBZOFRWACOVRX5KQM3CZIV/graph.json","events_json":"https://pith.science/api/pith-number/VXNLVBZOFRWACOVRX5KQM3CZIV/events.json","paper":"https://pith.science/paper/VXNLVBZO"},"agent_actions":{"view_html":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV","download_json":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV.json","view_paper":"https://pith.science/paper/VXNLVBZO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2007.12219&json=true","fetch_graph":"https://pith.science/api/pith-number/VXNLVBZOFRWACOVRX5KQM3CZIV/graph.json","fetch_events":"https://pith.science/api/pith-number/VXNLVBZOFRWACOVRX5KQM3CZIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV/action/storage_attestation","attest_author":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV/action/author_attestation","sign_citation":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV/action/citation_signature","submit_replication":"https://pith.science/pith/VXNLVBZOFRWACOVRX5KQM3CZIV/action/replication_record"}},"created_at":"2026-07-05T01:21:50.343459+00:00","updated_at":"2026-07-05T01:21:50.343459+00:00"}