{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:J74HZLOFL64IVTO7PK6TEF3NT5","short_pith_number":"pith:J74HZLOF","canonical_record":{"source":{"id":"1609.06660","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-21T18:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"2b07a15212721ece8082e39d8f4cd02a9cfc29bf75758ae6a5ec48591bb4340f","abstract_canon_sha256":"a944ea199d0ebbf21fdb7adb8365344539f8f6e155992d54aa5f02b6d77ba709"},"schema_version":"1.0"},"canonical_sha256":"4ff87cadc55fb88acddf7abd32176d9f57ce982cc95fffb590172efa3c16dd0d","source":{"kind":"arxiv","id":"1609.06660","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06660","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06660v2","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06660","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"J74HZLOFL64I","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J74HZLOFL64IVTO7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J74HZLOF","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:J74HZLOFL64IVTO7PK6TEF3NT5","target":"record","payload":{"canonical_record":{"source":{"id":"1609.06660","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-21T18:19:21Z","cross_cats_sorted":[],"title_canon_sha256":"2b07a15212721ece8082e39d8f4cd02a9cfc29bf75758ae6a5ec48591bb4340f","abstract_canon_sha256":"a944ea199d0ebbf21fdb7adb8365344539f8f6e155992d54aa5f02b6d77ba709"},"schema_version":"1.0"},"canonical_sha256":"4ff87cadc55fb88acddf7abd32176d9f57ce982cc95fffb590172efa3c16dd0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:32.185715Z","signature_b64":"ZgAIXXni14REOdgmXe7fFTZ8HmLX6CCb+UJEYDsSbLHQPEsgIf/ss4qRHL8phtVfj0Wui3h6Swlf3FCopiy2AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ff87cadc55fb88acddf7abd32176d9f57ce982cc95fffb590172efa3c16dd0d","last_reissued_at":"2026-05-18T01:03:32.185111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:32.185111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.06660","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"46gR6SJHsobMw013wH1cB9+lbMyaXnXTjUbUc5GpLB21qIjFD7xqN92XRCelHpPnt5v5KIhTBX0A9nL6iAhJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:37:29.510307Z"},"content_sha256":"effa833df6295dfd74943e5743bf1a276cf700499dcba6e4d645d85be0c2f5cb","schema_version":"1.0","event_id":"sha256:effa833df6295dfd74943e5743bf1a276cf700499dcba6e4d645d85be0c2f5cb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:J74HZLOFL64IVTO7PK6TEF3NT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometric convergence rate of distributed economic dispatch/demand response in power networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alex Olshevsky, Thinh T. Doan","submitted_at":"2016-09-21T18:19:21Z","abstract_excerpt":"Motivated by potential applications in power systems, we study a problem of optimizing a sum of $n$ convex functions on dynamic networks of $n$ nodes when each function is known to only a single node. The nodes' variables, while satisfy their local constraints, are coupled through a linear constraint. Our main contribution is to design a fully distributed primal-dual method for this problem. Under some fairly standard assumptions on objective functions, strong convexity and smoothness, we provide an explicit analysis for the convergence rate of our method on different networks. In particular, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06660","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:03:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUBUDLy7m0/0Y4LnzZMs/qIq9mLwiLwxnTfuLgc/NXP33zd9NRo8Kz3bcjYt4RPkanZ7iIhqJLRkGLLqAXoLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:37:29.511013Z"},"content_sha256":"27acb3e52099a3c3db430c2f02b2630859084020418070592836615fb4a72376","schema_version":"1.0","event_id":"sha256:27acb3e52099a3c3db430c2f02b2630859084020418070592836615fb4a72376"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J74HZLOFL64IVTO7PK6TEF3NT5/bundle.json","state_url":"https://pith.science/pith/J74HZLOFL64IVTO7PK6TEF3NT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J74HZLOFL64IVTO7PK6TEF3NT5/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T00:37:29Z","links":{"resolver":"https://pith.science/pith/J74HZLOFL64IVTO7PK6TEF3NT5","bundle":"https://pith.science/pith/J74HZLOFL64IVTO7PK6TEF3NT5/bundle.json","state":"https://pith.science/pith/J74HZLOFL64IVTO7PK6TEF3NT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J74HZLOFL64IVTO7PK6TEF3NT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J74HZLOFL64IVTO7PK6TEF3NT5","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":"a944ea199d0ebbf21fdb7adb8365344539f8f6e155992d54aa5f02b6d77ba709","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-21T18:19:21Z","title_canon_sha256":"2b07a15212721ece8082e39d8f4cd02a9cfc29bf75758ae6a5ec48591bb4340f"},"schema_version":"1.0","source":{"id":"1609.06660","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.06660","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.06660v2","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.06660","created_at":"2026-05-18T01:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"J74HZLOFL64I","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J74HZLOFL64IVTO7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J74HZLOF","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:27acb3e52099a3c3db430c2f02b2630859084020418070592836615fb4a72376","target":"graph","created_at":"2026-05-18T01:03:32Z","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":"Motivated by potential applications in power systems, we study a problem of optimizing a sum of $n$ convex functions on dynamic networks of $n$ nodes when each function is known to only a single node. The nodes' variables, while satisfy their local constraints, are coupled through a linear constraint. Our main contribution is to design a fully distributed primal-dual method for this problem. Under some fairly standard assumptions on objective functions, strong convexity and smoothness, we provide an explicit analysis for the convergence rate of our method on different networks. In particular, ","authors_text":"Alex Olshevsky, Thinh T. Doan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-21T18:19:21Z","title":"On the geometric convergence rate of distributed economic dispatch/demand response in power networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06660","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:effa833df6295dfd74943e5743bf1a276cf700499dcba6e4d645d85be0c2f5cb","target":"record","created_at":"2026-05-18T01:03:32Z","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":"a944ea199d0ebbf21fdb7adb8365344539f8f6e155992d54aa5f02b6d77ba709","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-21T18:19:21Z","title_canon_sha256":"2b07a15212721ece8082e39d8f4cd02a9cfc29bf75758ae6a5ec48591bb4340f"},"schema_version":"1.0","source":{"id":"1609.06660","kind":"arxiv","version":2}},"canonical_sha256":"4ff87cadc55fb88acddf7abd32176d9f57ce982cc95fffb590172efa3c16dd0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ff87cadc55fb88acddf7abd32176d9f57ce982cc95fffb590172efa3c16dd0d","first_computed_at":"2026-05-18T01:03:32.185111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:32.185111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZgAIXXni14REOdgmXe7fFTZ8HmLX6CCb+UJEYDsSbLHQPEsgIf/ss4qRHL8phtVfj0Wui3h6Swlf3FCopiy2AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:32.185715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.06660","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:effa833df6295dfd74943e5743bf1a276cf700499dcba6e4d645d85be0c2f5cb","sha256:27acb3e52099a3c3db430c2f02b2630859084020418070592836615fb4a72376"],"state_sha256":"8b360be8138228276b0f88d1bf6d21a696fd8cc4c08485b3d9028e51525b0ade"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hh9AuYA40xP5duFbtHPkrVl2n476xnFsSleWy9rJaiuDtn9j6f2a9pyD0IIvA8FKAewFth1oy+sensO7p5sZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:37:29.514457Z","bundle_sha256":"faef9b6d55d352375b27b1db3af72db42751d5f7d18e442c6bd2b1d4bda01dc2"}}