{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:Q4DLHA5Z2UUTMTLQRP45CQI3WF","short_pith_number":"pith:Q4DLHA5Z","canonical_record":{"source":{"id":"2206.03041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-06-07T06:32:28Z","cross_cats_sorted":[],"title_canon_sha256":"bef922a1b33182e1c8bca70c30c87de9b4181ed6210b7782867125664a614afe","abstract_canon_sha256":"4e00dc3eff55d35dc4920e7fa83fdb3950ac2099b43978e918e694cf599469d0"},"schema_version":"1.0"},"canonical_sha256":"8706b383b9d529364d708bf9d1411bb1449c086c63078ae05e4fe4591b10e507","source":{"kind":"arxiv","id":"2206.03041","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.03041","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"2206.03041v2","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.03041","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q4DLHA5Z2UUT","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q4DLHA5Z2UUTMTLQ","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q4DLHA5Z","created_at":"2026-07-05T06:03:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:Q4DLHA5Z2UUTMTLQRP45CQI3WF","target":"record","payload":{"canonical_record":{"source":{"id":"2206.03041","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-06-07T06:32:28Z","cross_cats_sorted":[],"title_canon_sha256":"bef922a1b33182e1c8bca70c30c87de9b4181ed6210b7782867125664a614afe","abstract_canon_sha256":"4e00dc3eff55d35dc4920e7fa83fdb3950ac2099b43978e918e694cf599469d0"},"schema_version":"1.0"},"canonical_sha256":"8706b383b9d529364d708bf9d1411bb1449c086c63078ae05e4fe4591b10e507","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:03:24.177505Z","signature_b64":"peeKqE0zrK0mwoiGWF48M0k44PrwvuE/VKNK8OI92FyiLl9IKqi+p6fv9E4MxjM73Nk/KCxAN4bjRruk3kPsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8706b383b9d529364d708bf9d1411bb1449c086c63078ae05e4fe4591b10e507","last_reissued_at":"2026-07-05T06:03:24.177082Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:03:24.177082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.03041","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":"2026-07-05T06:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zKDEO5GDRt1zEq1I82GOTwG3xnStJmXlDcfIJcaV+B0M5AX955iBYcgqzp1tub69BzqO1JbbfNIRPSc9bE52Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:11:36.852958Z"},"content_sha256":"8288238062d995f3f428871906628f84d0e29a0890d9251bd703405c994ab8ce","schema_version":"1.0","event_id":"sha256:8288238062d995f3f428871906628f84d0e29a0890d9251bd703405c994ab8ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:Q4DLHA5Z2UUTMTLQRP45CQI3WF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic error bound of the smoothed gap and the restarted averaged primal-dual hybrid gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"IDS, IP Paris), Olivier Fercoq (S2A","submitted_at":"2022-06-07T06:32:28Z","abstract_excerpt":"We study the linear convergence of the primal-dual hybrid gradient method. After a review of current analyses, we show that they do not explain properly the behavior of the algorithm, even on the most simple problems. We thus introduce the quadratic error bound of the smoothed gap, a new regularity assumption that holds for a wide class of optimization problems. Equipped with this tool, we manage to prove tighter convergence rates. Then, we show that averaging and restarting the primal-dual hybrid gradient allows us to leverage better the regularity constant. Numerical experiments on linear an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.03041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.03041/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:03:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgDueHzD0UycOOnAWILT90ILvB3JLRUwSRe7Y9X/Y6Elw5UgMJ4NkS9hDDCgcSf3QWUKFB2a/79NFXep1uYbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:11:36.853461Z"},"content_sha256":"02eb12ce86f6b6571aaa47bcd0b7766dddf317134649244326cd540ef8cee54c","schema_version":"1.0","event_id":"sha256:02eb12ce86f6b6571aaa47bcd0b7766dddf317134649244326cd540ef8cee54c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/bundle.json","state_url":"https://pith.science/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/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":"2026-08-14T15:11:36Z","links":{"resolver":"https://pith.science/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF","bundle":"https://pith.science/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/bundle.json","state":"https://pith.science/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4DLHA5Z2UUTMTLQRP45CQI3WF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Q4DLHA5Z2UUTMTLQRP45CQI3WF","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":"4e00dc3eff55d35dc4920e7fa83fdb3950ac2099b43978e918e694cf599469d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-06-07T06:32:28Z","title_canon_sha256":"bef922a1b33182e1c8bca70c30c87de9b4181ed6210b7782867125664a614afe"},"schema_version":"1.0","source":{"id":"2206.03041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.03041","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"arxiv_version","alias_value":"2206.03041v2","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.03041","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q4DLHA5Z2UUT","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_16","alias_value":"Q4DLHA5Z2UUTMTLQ","created_at":"2026-07-05T06:03:24Z"},{"alias_kind":"pith_short_8","alias_value":"Q4DLHA5Z","created_at":"2026-07-05T06:03:24Z"}],"graph_snapshots":[{"event_id":"sha256:02eb12ce86f6b6571aaa47bcd0b7766dddf317134649244326cd540ef8cee54c","target":"graph","created_at":"2026-07-05T06:03:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.03041/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the linear convergence of the primal-dual hybrid gradient method. After a review of current analyses, we show that they do not explain properly the behavior of the algorithm, even on the most simple problems. We thus introduce the quadratic error bound of the smoothed gap, a new regularity assumption that holds for a wide class of optimization problems. Equipped with this tool, we manage to prove tighter convergence rates. Then, we show that averaging and restarting the primal-dual hybrid gradient allows us to leverage better the regularity constant. Numerical experiments on linear an","authors_text":"IDS, IP Paris), Olivier Fercoq (S2A","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-06-07T06:32:28Z","title":"Quadratic error bound of the smoothed gap and the restarted averaged primal-dual hybrid gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.03041","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":"sha256:8288238062d995f3f428871906628f84d0e29a0890d9251bd703405c994ab8ce","target":"record","created_at":"2026-07-05T06:03:24Z","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":"4e00dc3eff55d35dc4920e7fa83fdb3950ac2099b43978e918e694cf599469d0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-06-07T06:32:28Z","title_canon_sha256":"bef922a1b33182e1c8bca70c30c87de9b4181ed6210b7782867125664a614afe"},"schema_version":"1.0","source":{"id":"2206.03041","kind":"arxiv","version":2}},"canonical_sha256":"8706b383b9d529364d708bf9d1411bb1449c086c63078ae05e4fe4591b10e507","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8706b383b9d529364d708bf9d1411bb1449c086c63078ae05e4fe4591b10e507","first_computed_at":"2026-07-05T06:03:24.177082Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:24.177082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"peeKqE0zrK0mwoiGWF48M0k44PrwvuE/VKNK8OI92FyiLl9IKqi+p6fv9E4MxjM73Nk/KCxAN4bjRruk3kPsAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:24.177505Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.03041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8288238062d995f3f428871906628f84d0e29a0890d9251bd703405c994ab8ce","sha256:02eb12ce86f6b6571aaa47bcd0b7766dddf317134649244326cd540ef8cee54c"],"state_sha256":"5c12eabc4edd00fd6c5309351a972f8e32a449738620c6f93753550d7471eae0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QeJr0NvTqzqPoP/fnlCIFvY7D2M9WSmgn1IPtc+quXqCOVslVPPa0aycDX0pWWOUTFb1ltZtPOSpg6idzL0+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:11:36.858814Z","bundle_sha256":"91aa80bf34b6444bfd5a3176a5ae0ca1de758b0630254e94c6d0d5bdc92b3a6e"}}