{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6W677DEXVIOJZKOKR7QYVUGPSB","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":"389758633f856c26253723d31064c69dd522f3590324ed27d94c4e0394f87512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-07-13T15:57:52Z","title_canon_sha256":"91796275b61aeb2ce07e89e6affbc0cdc865095c109100f2e4655982022a6095"},"schema_version":"1.0","source":{"id":"2207.06304","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.06304","created_at":"2026-07-05T05:12:13Z"},{"alias_kind":"arxiv_version","alias_value":"2207.06304v3","created_at":"2026-07-05T05:12:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.06304","created_at":"2026-07-05T05:12:13Z"},{"alias_kind":"pith_short_12","alias_value":"6W677DEXVIOJ","created_at":"2026-07-05T05:12:13Z"},{"alias_kind":"pith_short_16","alias_value":"6W677DEXVIOJZKOK","created_at":"2026-07-05T05:12:13Z"},{"alias_kind":"pith_short_8","alias_value":"6W677DEX","created_at":"2026-07-05T05:12:13Z"}],"graph_snapshots":[{"event_id":"sha256:bd96136e6eb60f72d88484cd9fbac89b5f335a0b0136f3a9989f4d9dd9e89f2d","target":"graph","created_at":"2026-07-05T05:12:13Z","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/2207.06304/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well-known that the lower bound of iteration complexity for solving nonconvex unconstrained optimization problems is $\\Omega(1/\\epsilon^2)$, which can be achieved by standard gradient descent algorithm when the objective function is smooth. This lower bound still holds for nonconvex constrained problems, while it is still unknown whether a first-order method can achieve this lower bound. In this paper, we show that a simple single-loop first-order algorithm called smoothed proximal augmented Lagrangian method (ALM) can achieve such iteration complexity lower bound. The key technical cont","authors_text":"Jiawei Zhang, Wenqiang Pu, Zhi-Quan Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-07-13T15:57:52Z","title":"On the Iteration Complexity of Smoothed Proximal ALM for Nonconvex Optimization Problem with Convex Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.06304","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":"sha256:68b789d84987a9d931ca444c6f631682196d5133b49c391fcf67d27d08bbe574","target":"record","created_at":"2026-07-05T05:12:13Z","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":"389758633f856c26253723d31064c69dd522f3590324ed27d94c4e0394f87512","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-07-13T15:57:52Z","title_canon_sha256":"91796275b61aeb2ce07e89e6affbc0cdc865095c109100f2e4655982022a6095"},"schema_version":"1.0","source":{"id":"2207.06304","kind":"arxiv","version":3}},"canonical_sha256":"f5bdff8c97aa1c9ca9ca8fe18ad0cf904b790d69c60f5deeb428665a17928ded","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5bdff8c97aa1c9ca9ca8fe18ad0cf904b790d69c60f5deeb428665a17928ded","first_computed_at":"2026-07-05T05:12:13.781013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:12:13.781013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"96ad8K5j6K/GKyxa3mx/GIm0TaFmGDxH30mKJw5Y62c2NmSBEpRW1mC2oJtGon8ZMgGsrq6hw4LStuEJmIztAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:12:13.781464Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.06304","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68b789d84987a9d931ca444c6f631682196d5133b49c391fcf67d27d08bbe574","sha256:bd96136e6eb60f72d88484cd9fbac89b5f335a0b0136f3a9989f4d9dd9e89f2d"],"state_sha256":"ad99a032cbc8810a454572710ea2dd0b41531c6bec1994042bb844727ebf04a7"}