{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:6WSF2MLILAA7W56ESHFMDDVDLP","short_pith_number":"pith:6WSF2MLI","schema_version":"1.0","canonical_sha256":"f5a45d31685801fb77c491cac18ea35bfd70ec15052b70a4498fd700356249ca","source":{"kind":"arxiv","id":"2006.08048","version":1},"attestation_state":"computed","paper":{"title":"Iteration-complexity of an inexact proximal accelerated augmented Lagrangian method for solving linearly constrained smooth nonconvex composite optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hairong Wang, Jefferson G. Melo, Renato D.C. Monteiro","submitted_at":"2020-06-14T22:51:55Z","abstract_excerpt":"This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient (ACG) method followed by a suitable Lagrange multiplier update. It is shown that IPAAL generates an approximate stationary solution in at most ${\\cal O}(\\log(1/\\rho)/\\rho^{3})$ ACG iterations, where $\\rho>0$ is the given tolerance. It is also shown that "},"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":"2006.08048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-06-14T22:51:55Z","cross_cats_sorted":[],"title_canon_sha256":"b8586364e4dc4945e43b9f591f5d9a2a4d334e3893745a25bd57ec33788460a8","abstract_canon_sha256":"f296a77aca403d7e00f4cbd535363d1bff784017a0ac70f9d5fa5d780aa6c13b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:17.810481Z","signature_b64":"/WMTlt3s91fQ2bQUm0x2jSEmZ5muX0icuXITMHtd1oJN0jsPuxwaQmGK8SQOXI8bKwR0pOTWGgK07nyYDZXAAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5a45d31685801fb77c491cac18ea35bfd70ec15052b70a4498fd700356249ca","last_reissued_at":"2026-07-05T01:10:17.809980Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:17.809980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iteration-complexity of an inexact proximal accelerated augmented Lagrangian method for solving linearly constrained smooth nonconvex composite optimization problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hairong Wang, Jefferson G. Melo, Renato D.C. Monteiro","submitted_at":"2020-06-14T22:51:55Z","abstract_excerpt":"This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient (ACG) method followed by a suitable Lagrange multiplier update. It is shown that IPAAL generates an approximate stationary solution in at most ${\\cal O}(\\log(1/\\rho)/\\rho^{3})$ ACG iterations, where $\\rho>0$ is the given tolerance. It is also shown that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.08048","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/2006.08048/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":"2006.08048","created_at":"2026-07-05T01:10:17.810064+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.08048v1","created_at":"2026-07-05T01:10:17.810064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.08048","created_at":"2026-07-05T01:10:17.810064+00:00"},{"alias_kind":"pith_short_12","alias_value":"6WSF2MLILAA7","created_at":"2026-07-05T01:10:17.810064+00:00"},{"alias_kind":"pith_short_16","alias_value":"6WSF2MLILAA7W56E","created_at":"2026-07-05T01:10:17.810064+00:00"},{"alias_kind":"pith_short_8","alias_value":"6WSF2MLI","created_at":"2026-07-05T01:10:17.810064+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2407.09927","citing_title":"An Adaptive Proximal ADMM for Nonconvex Linearly Constrained Composite Programs","ref_index":39,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP","json":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP.json","graph_json":"https://pith.science/api/pith-number/6WSF2MLILAA7W56ESHFMDDVDLP/graph.json","events_json":"https://pith.science/api/pith-number/6WSF2MLILAA7W56ESHFMDDVDLP/events.json","paper":"https://pith.science/paper/6WSF2MLI"},"agent_actions":{"view_html":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP","download_json":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP.json","view_paper":"https://pith.science/paper/6WSF2MLI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.08048&json=true","fetch_graph":"https://pith.science/api/pith-number/6WSF2MLILAA7W56ESHFMDDVDLP/graph.json","fetch_events":"https://pith.science/api/pith-number/6WSF2MLILAA7W56ESHFMDDVDLP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP/action/storage_attestation","attest_author":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP/action/author_attestation","sign_citation":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP/action/citation_signature","submit_replication":"https://pith.science/pith/6WSF2MLILAA7W56ESHFMDDVDLP/action/replication_record"}},"created_at":"2026-07-05T01:10:17.810064+00:00","updated_at":"2026-07-05T01:10:17.810064+00:00"}