{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7KMOEXGV25MVXUBV32XET5C35O","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":"1ee500f56f5285fe509387e23bb18313298aa04d09aead3c2d76b84aea568a0a","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-15T05:12:48Z","title_canon_sha256":"6535999c8c42aeebaf2214496d35a8825e577f84f60a8fe0f7d437897b09461a"},"schema_version":"1.0","source":{"id":"1001.2612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.2612","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1001.2612v2","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.2612","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"7KMOEXGV25MV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7KMOEXGV25MVXUBV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7KMOEXGV","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:3bdf4b085d35e75c07d2cf93b9944696eb68f67182d9fe9be5e0971eb93e0649","target":"graph","created_at":"2026-05-18T04:22:11Z","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":"We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorith","authors_text":"Minghui Zhu, Sonia Martinez","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-15T05:12:48Z","title":"On distributed convex optimization under inequality and equality constraints via primal-dual subgradient methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.2612","kind":"arxiv","version":2},"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:ad13593136843c650f3e9ab8ebdbc4398d5cf54d362327e58f9904ccfb5ef882","target":"record","created_at":"2026-05-18T04:22:11Z","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":"1ee500f56f5285fe509387e23bb18313298aa04d09aead3c2d76b84aea568a0a","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-01-15T05:12:48Z","title_canon_sha256":"6535999c8c42aeebaf2214496d35a8825e577f84f60a8fe0f7d437897b09461a"},"schema_version":"1.0","source":{"id":"1001.2612","kind":"arxiv","version":2}},"canonical_sha256":"fa98e25cd5d7595bd035deae49f45beb90288d407980fea7091c065ed48e7194","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa98e25cd5d7595bd035deae49f45beb90288d407980fea7091c065ed48e7194","first_computed_at":"2026-05-18T04:22:11.547779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:11.547779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R7fqnN6cyQRaApMX0HlmEAAOt0/t2Mr93ZQUtuD9VZLOaWUuXCR4iFdp/IxEhgaX5qYTAy7nCThPDTtPeRMQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:11.548145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.2612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad13593136843c650f3e9ab8ebdbc4398d5cf54d362327e58f9904ccfb5ef882","sha256:3bdf4b085d35e75c07d2cf93b9944696eb68f67182d9fe9be5e0971eb93e0649"],"state_sha256":"d19b2dc464bfb4d28c94ec9b1470e077d64f1b37a518bb9c5221072d7372ab3d"}