{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EVOYNFXJAV5MNV3GRMRSC73IQ6","short_pith_number":"pith:EVOYNFXJ","canonical_record":{"source":{"id":"1509.08007","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-26T16:41:58Z","cross_cats_sorted":[],"title_canon_sha256":"c86bd14ad8c80af9a5c71619fbc4bd5bb56802704cfc91c7ad137d35f8b680c6","abstract_canon_sha256":"bdd1ac0b0d7f73e20f5c65259a63f981b6fd0b4a49cf4d12a7179c65488723fc"},"schema_version":"1.0"},"canonical_sha256":"255d8696e9057ac6d7668b23217f68878cdd6920ac44d8d0f0bac262b78cac97","source":{"kind":"arxiv","id":"1509.08007","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08007","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08007v3","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08007","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"EVOYNFXJAV5M","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EVOYNFXJAV5MNV3G","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EVOYNFXJ","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EVOYNFXJAV5MNV3GRMRSC73IQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1509.08007","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-26T16:41:58Z","cross_cats_sorted":[],"title_canon_sha256":"c86bd14ad8c80af9a5c71619fbc4bd5bb56802704cfc91c7ad137d35f8b680c6","abstract_canon_sha256":"bdd1ac0b0d7f73e20f5c65259a63f981b6fd0b4a49cf4d12a7179c65488723fc"},"schema_version":"1.0"},"canonical_sha256":"255d8696e9057ac6d7668b23217f68878cdd6920ac44d8d0f0bac262b78cac97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:35.106301Z","signature_b64":"2l9hBgwIIY8q/hcjO3c6T9Yd5hfHEZAtjhtEQVChdy9r8hC23KzQyFlacg0nHR5l0xDdkBJRx5zmFv0Su0RfAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"255d8696e9057ac6d7668b23217f68878cdd6920ac44d8d0f0bac262b78cac97","last_reissued_at":"2026-05-18T00:25:35.105691Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:35.105691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.08007","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L+2eeoecIJclNHAXCyMwjD1jkOz8Gscrj17oa4S9/kvlMjq9+WtYgR1ZAxvRv5fCoy1o3dnhuDlzBdGV5lWWCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:15:49.152073Z"},"content_sha256":"58f839a7bd09facee10653129b9dcb81e10beb5662a9334c8847a6ab07e981db","schema_version":"1.0","event_id":"sha256:58f839a7bd09facee10653129b9dcb81e10beb5662a9334c8847a6ab07e981db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EVOYNFXJAV5MNV3GRMRSC73IQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Projection Methods for Decentralized Optimization with Functional Constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Michael M. Zavlanos, Soomin Lee","submitted_at":"2015-09-26T16:41:58Z","abstract_excerpt":"We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive algorithm which is based on the concept of approximate projections. Our algorithm is one of the consensus based methods in that, at every iteration, each agent performs a consensus update of its decision variables followed by an optimization step of its local objective function and local constraints. Unlike other methods, the last step of our method is not an "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08007","kind":"arxiv","version":3},"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":"2026-05-18T00:25:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUqCalY4wTFwd6YfX18VObnsvYLNGXQ5dlIV7V+j/LZtgTjhosaiJC74PJWA0Z6avFp3qXlPOZmzGLzB4foGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:15:49.152434Z"},"content_sha256":"3055b797d0d37a40133ee0ca7e65b51b9e1bb7752ce950309b5bdf59d59c64a0","schema_version":"1.0","event_id":"sha256:3055b797d0d37a40133ee0ca7e65b51b9e1bb7752ce950309b5bdf59d59c64a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/bundle.json","state_url":"https://pith.science/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/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":"2026-05-28T02:15:49Z","links":{"resolver":"https://pith.science/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6","bundle":"https://pith.science/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/bundle.json","state":"https://pith.science/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVOYNFXJAV5MNV3GRMRSC73IQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EVOYNFXJAV5MNV3GRMRSC73IQ6","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":"bdd1ac0b0d7f73e20f5c65259a63f981b6fd0b4a49cf4d12a7179c65488723fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-26T16:41:58Z","title_canon_sha256":"c86bd14ad8c80af9a5c71619fbc4bd5bb56802704cfc91c7ad137d35f8b680c6"},"schema_version":"1.0","source":{"id":"1509.08007","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.08007","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"arxiv_version","alias_value":"1509.08007v3","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.08007","created_at":"2026-05-18T00:25:35Z"},{"alias_kind":"pith_short_12","alias_value":"EVOYNFXJAV5M","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EVOYNFXJAV5MNV3G","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EVOYNFXJ","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:3055b797d0d37a40133ee0ca7e65b51b9e1bb7752ce950309b5bdf59d59c64a0","target":"graph","created_at":"2026-05-18T00:25:35Z","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 distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as Linear Matrix Inequalities (LMIs). We propose a decentralized and computationally inexpensive algorithm which is based on the concept of approximate projections. Our algorithm is one of the consensus based methods in that, at every iteration, each agent performs a consensus update of its decision variables followed by an optimization step of its local objective function and local constraints. Unlike other methods, the last step of our method is not an ","authors_text":"Michael M. Zavlanos, Soomin Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-26T16:41:58Z","title":"Approximate Projection Methods for Decentralized Optimization with Functional Constraints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08007","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":"sha256:58f839a7bd09facee10653129b9dcb81e10beb5662a9334c8847a6ab07e981db","target":"record","created_at":"2026-05-18T00:25:35Z","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":"bdd1ac0b0d7f73e20f5c65259a63f981b6fd0b4a49cf4d12a7179c65488723fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-09-26T16:41:58Z","title_canon_sha256":"c86bd14ad8c80af9a5c71619fbc4bd5bb56802704cfc91c7ad137d35f8b680c6"},"schema_version":"1.0","source":{"id":"1509.08007","kind":"arxiv","version":3}},"canonical_sha256":"255d8696e9057ac6d7668b23217f68878cdd6920ac44d8d0f0bac262b78cac97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"255d8696e9057ac6d7668b23217f68878cdd6920ac44d8d0f0bac262b78cac97","first_computed_at":"2026-05-18T00:25:35.105691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:35.105691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2l9hBgwIIY8q/hcjO3c6T9Yd5hfHEZAtjhtEQVChdy9r8hC23KzQyFlacg0nHR5l0xDdkBJRx5zmFv0Su0RfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:35.106301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.08007","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58f839a7bd09facee10653129b9dcb81e10beb5662a9334c8847a6ab07e981db","sha256:3055b797d0d37a40133ee0ca7e65b51b9e1bb7752ce950309b5bdf59d59c64a0"],"state_sha256":"1e3a16fe4e262672fadf2f0d45111c8d5fc6a8f9f98143b0d7cb03fb0a933da0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MB4QHqIN6njwVSzDvOtYWdBDppCkLb2O3/IjDOmrkYzJllJKkjHN3CTF3zIMGN9evCQ7Zw9GjpOOyUCS42FdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:15:49.154366Z","bundle_sha256":"0d1931092f9baa43bd560e439ed4bbe205bc3d7d460979b1584477b0d37dc024"}}