{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LBLOHVVXTCZZZVSDBXFFQ3UIUL","short_pith_number":"pith:LBLOHVVX","canonical_record":{"source":{"id":"1808.08287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-24T19:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"c48b185343a6073f623bdd5e00452351e1325d365f8a9681e017f9b38a2eb566","abstract_canon_sha256":"041358b83c035697c7afdc9608911e360a48274439206f54758f7ec59b92b8bc"},"schema_version":"1.0"},"canonical_sha256":"5856e3d6b798b39cd6430dca586e88a2cc1a65244d4f51169a29b917dc8492fd","source":{"kind":"arxiv","id":"1808.08287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08287","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08287v1","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08287","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"LBLOHVVXTCZZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LBLOHVVXTCZZZVSD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LBLOHVVX","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LBLOHVVXTCZZZVSDBXFFQ3UIUL","target":"record","payload":{"canonical_record":{"source":{"id":"1808.08287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-24T19:45:19Z","cross_cats_sorted":[],"title_canon_sha256":"c48b185343a6073f623bdd5e00452351e1325d365f8a9681e017f9b38a2eb566","abstract_canon_sha256":"041358b83c035697c7afdc9608911e360a48274439206f54758f7ec59b92b8bc"},"schema_version":"1.0"},"canonical_sha256":"5856e3d6b798b39cd6430dca586e88a2cc1a65244d4f51169a29b917dc8492fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:21.581679Z","signature_b64":"TAU6Ika6P44hnFq4pJ3PVyZi/SghfW1xOIuDuc9dk3NmxlBnbLxs7YpVcZxV1me3Hp4axdunQt+uYlE8gBQTBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5856e3d6b798b39cd6430dca586e88a2cc1a65244d4f51169a29b917dc8492fd","last_reissued_at":"2026-05-18T00:07:21.580969Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:21.580969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.08287","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dz06rPVh4p089B9ZSfBj3iFaisOwBJKnJvYXHxgL9Igh3D9CtU/CLM+OYvoyyC4Vob1ka7yohnDoMwDWiNh2DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:25:03.500567Z"},"content_sha256":"e3859c9bb690e4a0196e039679b75cf31cac41c389f1b05dd2a4df7c835805df","schema_version":"1.0","event_id":"sha256:e3859c9bb690e4a0196e039679b75cf31cac41c389f1b05dd2a4df7c835805df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LBLOHVVXTCZZZVSDBXFFQ3UIUL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of the Augmented Decomposition Algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hongsheng Liu, Shu Lu","submitted_at":"2018-08-24T19:45:19Z","abstract_excerpt":"We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA is o(1/k) under the assumption that there exists a saddle point. We consider the inexact Augmented Decomposition Algorithm (iADA) and establish global and local convergence results under some mild assumptions, by providing a stability result for the maximal monotone operator T associated with the perturbation from both primal and dual perspectives. This res"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08287","kind":"arxiv","version":1},"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":"2026-05-18T00:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HF9MXavRjqCUBenaD6kuITp+u5RDP3UmC5M9ji5hDlWneGgItP4DP0iOSa0jqVIJ0Gx0XQ7kV7/5zVLzvslbDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:25:03.501211Z"},"content_sha256":"c339c8777acedad880ba6b7d936d45731f04a3b132df12c3dd6e28cdb4345b63","schema_version":"1.0","event_id":"sha256:c339c8777acedad880ba6b7d936d45731f04a3b132df12c3dd6e28cdb4345b63"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/bundle.json","state_url":"https://pith.science/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/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":"2026-05-27T13:25:03Z","links":{"resolver":"https://pith.science/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL","bundle":"https://pith.science/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/bundle.json","state":"https://pith.science/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBLOHVVXTCZZZVSDBXFFQ3UIUL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LBLOHVVXTCZZZVSDBXFFQ3UIUL","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":"041358b83c035697c7afdc9608911e360a48274439206f54758f7ec59b92b8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-24T19:45:19Z","title_canon_sha256":"c48b185343a6073f623bdd5e00452351e1325d365f8a9681e017f9b38a2eb566"},"schema_version":"1.0","source":{"id":"1808.08287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.08287","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1808.08287v1","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.08287","created_at":"2026-05-18T00:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"LBLOHVVXTCZZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"LBLOHVVXTCZZZVSD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"LBLOHVVX","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c339c8777acedad880ba6b7d936d45731f04a3b132df12c3dd6e28cdb4345b63","target":"graph","created_at":"2026-05-18T00:07:21Z","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 study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA is o(1/k) under the assumption that there exists a saddle point. We consider the inexact Augmented Decomposition Algorithm (iADA) and establish global and local convergence results under some mild assumptions, by providing a stability result for the maximal monotone operator T associated with the perturbation from both primal and dual perspectives. This res","authors_text":"Hongsheng Liu, Shu Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-24T19:45:19Z","title":"Convergence of the Augmented Decomposition Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.08287","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:e3859c9bb690e4a0196e039679b75cf31cac41c389f1b05dd2a4df7c835805df","target":"record","created_at":"2026-05-18T00:07:21Z","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":"041358b83c035697c7afdc9608911e360a48274439206f54758f7ec59b92b8bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-08-24T19:45:19Z","title_canon_sha256":"c48b185343a6073f623bdd5e00452351e1325d365f8a9681e017f9b38a2eb566"},"schema_version":"1.0","source":{"id":"1808.08287","kind":"arxiv","version":1}},"canonical_sha256":"5856e3d6b798b39cd6430dca586e88a2cc1a65244d4f51169a29b917dc8492fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5856e3d6b798b39cd6430dca586e88a2cc1a65244d4f51169a29b917dc8492fd","first_computed_at":"2026-05-18T00:07:21.580969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:21.580969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TAU6Ika6P44hnFq4pJ3PVyZi/SghfW1xOIuDuc9dk3NmxlBnbLxs7YpVcZxV1me3Hp4axdunQt+uYlE8gBQTBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:21.581679Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.08287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3859c9bb690e4a0196e039679b75cf31cac41c389f1b05dd2a4df7c835805df","sha256:c339c8777acedad880ba6b7d936d45731f04a3b132df12c3dd6e28cdb4345b63"],"state_sha256":"43bc90a671cb6044fc9034b6a5c69589e9a531a21d86189ec377e5c9a3039c12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqofzZOfgIUG8YKla+d08zhrfohnaSLFbQq4ucZkbKwuMcE9ZYWI4yZPMorwHDX06wsLK1qSyx/9ZA3Aqqp1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:25:03.504433Z","bundle_sha256":"9eb286fc79b3fbbd4350b52625128019b10eed222f4c9e5b8f3fa77664549d4b"}}