{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:CEKRN452CFAJ3AHKBQV24URFH6","short_pith_number":"pith:CEKRN452","schema_version":"1.0","canonical_sha256":"111516f3ba11409d80ea0c2bae52253fbdcdf5112755c3c04b68bcb4cbbc9b0c","source":{"kind":"arxiv","id":"2304.02459","version":1},"attestation_state":"computed","paper":{"title":"Lagrangian-based methods in convex optimization: prediction-correction frameworks with non-ergodic convergence rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Shiru Li, Tao Zhang, Yong Xia","submitted_at":"2023-04-05T14:37:21Z","abstract_excerpt":"Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic convergence rates for general convex optimization and $O(1/k^2)$ non-ergodic convergence rates under the assumption that the objective function is strongly convex or gradient Lipschitz continuous. We give two approaches ($updating~multiplier~once$ $or~twice$) to design algorithms satisfying the presented prediction-correction frameworks. As applications, we"},"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":"2304.02459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-04-05T14:37:21Z","cross_cats_sorted":[],"title_canon_sha256":"5309f5dd80e4b5b8763b53e74b64e82f9b62f3c58ce39c0bbb2a26070ec5040b","abstract_canon_sha256":"4fb6b290050a78dd433750fe9b43ed9f3283a5e934095e55bdd68d504479ea9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:58:25.781640Z","signature_b64":"108jZty8kWX7J0+nx5BUtDPxKIaYADCOjwGkUM713+zpNF2XmVNrrqBbN+Su46SBWc9zl39CIk4HPXJSx1BYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"111516f3ba11409d80ea0c2bae52253fbdcdf5112755c3c04b68bcb4cbbc9b0c","last_reissued_at":"2026-07-05T05:58:25.781282Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:58:25.781282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lagrangian-based methods in convex optimization: prediction-correction frameworks with non-ergodic convergence rates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Shiru Li, Tao Zhang, Yong Xia","submitted_at":"2023-04-05T14:37:21Z","abstract_excerpt":"Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic convergence rates for general convex optimization and $O(1/k^2)$ non-ergodic convergence rates under the assumption that the objective function is strongly convex or gradient Lipschitz continuous. We give two approaches ($updating~multiplier~once$ $or~twice$) to design algorithms satisfying the presented prediction-correction frameworks. As applications, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.02459","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/2304.02459/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":"2304.02459","created_at":"2026-07-05T05:58:25.781345+00:00"},{"alias_kind":"arxiv_version","alias_value":"2304.02459v1","created_at":"2026-07-05T05:58:25.781345+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.02459","created_at":"2026-07-05T05:58:25.781345+00:00"},{"alias_kind":"pith_short_12","alias_value":"CEKRN452CFAJ","created_at":"2026-07-05T05:58:25.781345+00:00"},{"alias_kind":"pith_short_16","alias_value":"CEKRN452CFAJ3AHK","created_at":"2026-07-05T05:58:25.781345+00:00"},{"alias_kind":"pith_short_8","alias_value":"CEKRN452","created_at":"2026-07-05T05:58:25.781345+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.20991","citing_title":"An accelerated semi-proximal ADMM with applications to multi-block sparse optimization problems","ref_index":24,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6","json":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6.json","graph_json":"https://pith.science/api/pith-number/CEKRN452CFAJ3AHKBQV24URFH6/graph.json","events_json":"https://pith.science/api/pith-number/CEKRN452CFAJ3AHKBQV24URFH6/events.json","paper":"https://pith.science/paper/CEKRN452"},"agent_actions":{"view_html":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6","download_json":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6.json","view_paper":"https://pith.science/paper/CEKRN452","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2304.02459&json=true","fetch_graph":"https://pith.science/api/pith-number/CEKRN452CFAJ3AHKBQV24URFH6/graph.json","fetch_events":"https://pith.science/api/pith-number/CEKRN452CFAJ3AHKBQV24URFH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6/action/storage_attestation","attest_author":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6/action/author_attestation","sign_citation":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6/action/citation_signature","submit_replication":"https://pith.science/pith/CEKRN452CFAJ3AHKBQV24URFH6/action/replication_record"}},"created_at":"2026-07-05T05:58:25.781345+00:00","updated_at":"2026-07-05T05:58:25.781345+00:00"}