{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BWIVPYWSTB5HFYRMVZAS37673H","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":"b063646ff1270cd9554951acd0855c30ce346597eb07d0cb9660a74edcd341c7","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-15T10:16:41Z","title_canon_sha256":"0f7e6b6c28ca35177ae72da89062eec1ff13ca1bd32b3a73dea9529196ddd1e5"},"schema_version":"1.0","source":{"id":"1711.05486","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05486","created_at":"2026-05-17T23:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05486v3","created_at":"2026-05-17T23:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05486","created_at":"2026-05-17T23:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"BWIVPYWSTB5H","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BWIVPYWSTB5HFYRM","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BWIVPYWS","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:70e84a8403543b6766d4fa41810ec9dca5f97006938c574992e6342055574703","target":"graph","created_at":"2026-05-17T23:44:10Z","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 group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose topology is described by a time-invariant directed graph, by combining saddle-point dynamics with Lie bracket approximation techniques we derive a methodology that allows to design distributed continuous-time optimization algorithms that solve this problem under minimal assumptions on the graph topology as well as on the structure of the constraints. We discuss","authors_text":"Bahman Gharesifard, Christian Ebenbauer, Simon Michalowsky","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-15T10:16:41Z","title":"A Lie bracket approximation approach to distributed optimization over directed graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05486","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:b91e9834d4ec8f67f6442a1ebd6e675e28f18b2da4af70469fd3cf0525788cfd","target":"record","created_at":"2026-05-17T23:44:10Z","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":"b063646ff1270cd9554951acd0855c30ce346597eb07d0cb9660a74edcd341c7","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-11-15T10:16:41Z","title_canon_sha256":"0f7e6b6c28ca35177ae72da89062eec1ff13ca1bd32b3a73dea9529196ddd1e5"},"schema_version":"1.0","source":{"id":"1711.05486","kind":"arxiv","version":3}},"canonical_sha256":"0d9157e2d2987a72e22cae412dffdfd9d7d3a6be18c309a40f5928d8790ac2d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d9157e2d2987a72e22cae412dffdfd9d7d3a6be18c309a40f5928d8790ac2d6","first_computed_at":"2026-05-17T23:44:10.330519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:10.330519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hUs50oxxluuQ8daKCL1LlKwB1ZesE25vZTUWieq/tBwaho26NqDaBZsIHrdWs0rwbchqDvKNkOGre6Bql3DUDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:10.331513Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05486","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b91e9834d4ec8f67f6442a1ebd6e675e28f18b2da4af70469fd3cf0525788cfd","sha256:70e84a8403543b6766d4fa41810ec9dca5f97006938c574992e6342055574703"],"state_sha256":"e4e60f7db2edde6080c3214d6ddf3fc9e23929362a895e275c0e65a8f610799f"}