{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y4BM7NPR3FHG6D6TFWBIKJMR65","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":"9ad0926ae9dffececae028cd9e48498216447f07157fdf77551437fd3e33dcea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-09T18:33:49Z","title_canon_sha256":"3168d2c6259493538fbcf46ca84d391caa6d83e99bc5db49ad402cfc20801153"},"schema_version":"1.0","source":{"id":"1309.2251","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2251","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2251v1","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2251","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"Y4BM7NPR3FHG","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y4BM7NPR3FHG6D6T","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y4BM7NPR","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:8ac413d75f8e2c1c3a7a9842ae7fe45f8d7aed349a3a4a96fc0dcf5ce27c070e","target":"graph","created_at":"2026-05-18T03:13:46Z","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"},"paper":{"abstract_excerpt":"In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent algorithms for solving these formulations. Moreover, we introduce a bundle-level method which converges linearly uniformly for both smooth and non-smooth problems and does not require any smoothness information. The convergence properties of these algorithms are also discussed. Finally, we consider a special case of LMIs, linear system of inequalities, and show","authors_text":"Cong D. Dang, Guanghui Lan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-09T18:33:49Z","title":"Linearly Convergent First-Order Algorithms for Semi-definite Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2251","kind":"arxiv","version":1},"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":"sha256:7b76f509025d5989dd83415851d1eeb6de5b4bb2aa22e674feb53864ac4fa632","target":"record","created_at":"2026-05-18T03:13:46Z","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":"9ad0926ae9dffececae028cd9e48498216447f07157fdf77551437fd3e33dcea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-09-09T18:33:49Z","title_canon_sha256":"3168d2c6259493538fbcf46ca84d391caa6d83e99bc5db49ad402cfc20801153"},"schema_version":"1.0","source":{"id":"1309.2251","kind":"arxiv","version":1}},"canonical_sha256":"c702cfb5f1d94e6f0fd32d82852591f75a5ff826e267c1d48f31209f173aaa8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c702cfb5f1d94e6f0fd32d82852591f75a5ff826e267c1d48f31209f173aaa8d","first_computed_at":"2026-05-18T03:13:46.828533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:46.828533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"quupx1YpMTx44iWn00cv0J5EeefX8HtuR3b6SRH/GCUo1TQQx74PqT7BXyJdsgeO9zpGzoKeQtfWvb6qxkDrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:46.829221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2251","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b76f509025d5989dd83415851d1eeb6de5b4bb2aa22e674feb53864ac4fa632","sha256:8ac413d75f8e2c1c3a7a9842ae7fe45f8d7aed349a3a4a96fc0dcf5ce27c070e"],"state_sha256":"4a2a276cd7ce7b127080f21e87b720d9cf67632187bde8088053f6cf87782cf7"}