{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QMB4KMKA45VPQ6U5LRK6FVF6Y6","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":"5c13ab42a6d608d732fe45fafc8be33cda5af9a1962ffa622e89e5875c122c71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-22T00:17:38Z","title_canon_sha256":"d1e924af3ae8d4f6af7caeda6c9a883f669003ab3070e76ea658f7fe98dc6c1e"},"schema_version":"1.0","source":{"id":"1702.06626","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.06626","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1702.06626v2","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.06626","created_at":"2026-05-18T00:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"QMB4KMKA45VP","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QMB4KMKA45VPQ6U5","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QMB4KMKA","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:1dc47ad4b840ac6db7afd66dac8f7333a2c21d98cbdcefd4c0df0da3db021b11","target":"graph","created_at":"2026-05-18T00:45:02Z","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":"In this paper, we obtain global $\\mathcal{O} (1/ \\sqrt{k})$ pointwise and $\\mathcal{O} (1/ {k})$ ergodic convergence rates for a variable metric proximal alternating direction method of multipliers(VM-PADMM) for solving linearly constrained convex optimization problems. The VM-PADMM can be seen as a class of ADMM variants, allowing the use of degenerate metrics (defined by noninvertible linear operators). We first propose and study nonasymptotic convergence rates of a variable metric hybrid proximal extragradient (VM-HPE) framework for solving monotone inclusions. Then, the above-mentioned con","authors_text":"Jefferson G. Melo, Max L.N. Goncalves, M. Marques Alves","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-22T00:17:38Z","title":"Pointwise and ergodic convergence rates of a variable metric proximal ADMM"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06626","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":"sha256:21c0a6b7805404f8e87647a450ebaf866b96d9861a0cfba8ac4615f07b47bda1","target":"record","created_at":"2026-05-18T00:45:02Z","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":"5c13ab42a6d608d732fe45fafc8be33cda5af9a1962ffa622e89e5875c122c71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-02-22T00:17:38Z","title_canon_sha256":"d1e924af3ae8d4f6af7caeda6c9a883f669003ab3070e76ea658f7fe98dc6c1e"},"schema_version":"1.0","source":{"id":"1702.06626","kind":"arxiv","version":2}},"canonical_sha256":"8303c53140e76af87a9d5c55e2d4bec782473f1140360507d7ca33e73d8581cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8303c53140e76af87a9d5c55e2d4bec782473f1140360507d7ca33e73d8581cd","first_computed_at":"2026-05-18T00:45:02.534824Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:02.534824Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+NMbqrX0nmc6lDyivpM0Zi6mMQuWNgTzZ6YtSxpLyeYtDuTgQunoou++qrar7MCCeEUd7myQPj0Se5WHiCn+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:02.535208Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.06626","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21c0a6b7805404f8e87647a450ebaf866b96d9861a0cfba8ac4615f07b47bda1","sha256:1dc47ad4b840ac6db7afd66dac8f7333a2c21d98cbdcefd4c0df0da3db021b11"],"state_sha256":"2329bd82d0a07c1cddcbae3104f0517de125004cbde34bcc27115f9474cdd64b"}