{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NJINKD24XIV3UWA67UKDAJLFWX","short_pith_number":"pith:NJINKD24","canonical_record":{"source":{"id":"2204.00502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-01T15:01:01Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"d40bd8b8bc507c63764718ce12e8dfa95c9625c972ec24cc0c129906683e9494","abstract_canon_sha256":"b1048a6577bcc16e92f7e7c41a4857769794f294d20f4185a0378bc6cfddfac1"},"schema_version":"1.0"},"canonical_sha256":"6a50d50f5cba2bba581efd14302565b5fbc0d64e2b4f3d2c9346a47dc3949b3c","source":{"kind":"arxiv","id":"2204.00502","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.00502","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"2204.00502v2","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00502","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"NJINKD24XIV3","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_16","alias_value":"NJINKD24XIV3UWA6","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_8","alias_value":"NJINKD24","created_at":"2026-07-05T04:55:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NJINKD24XIV3UWA67UKDAJLFWX","target":"record","payload":{"canonical_record":{"source":{"id":"2204.00502","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-01T15:01:01Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"d40bd8b8bc507c63764718ce12e8dfa95c9625c972ec24cc0c129906683e9494","abstract_canon_sha256":"b1048a6577bcc16e92f7e7c41a4857769794f294d20f4185a0378bc6cfddfac1"},"schema_version":"1.0"},"canonical_sha256":"6a50d50f5cba2bba581efd14302565b5fbc0d64e2b4f3d2c9346a47dc3949b3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:55:51.537060Z","signature_b64":"w7NgWs9sLFE/iKlRhLg4PgxEqW31nWaDfCbBDRkTZMiiSjCGU4SvGrVGvRySwGSCcJ7F1RfwNnuWZbz7bdGtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a50d50f5cba2bba581efd14302565b5fbc0d64e2b4f3d2c9346a47dc3949b3c","last_reissued_at":"2026-07-05T04:55:51.536572Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:55:51.536572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2204.00502","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":"2026-07-05T04:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TlN2udL1tsHRg/6IcSrjXJP1eaToE41YV1q3oIlP6LsJ1KTv6xVLE+TbMkV1iNojmDap7zuy62hWrweVQQdsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:20:50.522013Z"},"content_sha256":"53e9d2ebccfe69339cfcce637a97959958bfd197dd7b91fff0650d80f30540b5","schema_version":"1.0","event_id":"sha256:53e9d2ebccfe69339cfcce637a97959958bfd197dd7b91fff0650d80f30540b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NJINKD24XIV3UWA67UKDAJLFWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Rate Bounds for the Mirror Descent Method: IQCs and the Bregman Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Ioannis Lestas, Khaled Laib, Mengmou Li","submitted_at":"2022-04-01T15:01:01Z","abstract_excerpt":"This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence rate of the MD method with strongly convex objective functions in both continuous-time and discrete-time. We formulate the problem of finding convergence rates of the MD algorithms into feasibility problems of linear matrix inequalities (LMIs) in both schemes. In particular, in continuous-time, we show that the Bregman divergence function, which is commonly u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00502","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/2204.00502/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":"2026-07-05T04:55:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7PzDmJd9ZGFL5z/dToVl4YCH9XlBefIQzX23ZBu885mamXQIVadoTTZ43cLvyca44JuaGzLjsCtpgQHatyGCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T02:20:50.522559Z"},"content_sha256":"873a08f444a8d67ef6a6f69cb8f73224944226e6648878ebb4e1182df0096a00","schema_version":"1.0","event_id":"sha256:873a08f444a8d67ef6a6f69cb8f73224944226e6648878ebb4e1182df0096a00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJINKD24XIV3UWA67UKDAJLFWX/bundle.json","state_url":"https://pith.science/pith/NJINKD24XIV3UWA67UKDAJLFWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJINKD24XIV3UWA67UKDAJLFWX/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":"2026-08-11T02:20:50Z","links":{"resolver":"https://pith.science/pith/NJINKD24XIV3UWA67UKDAJLFWX","bundle":"https://pith.science/pith/NJINKD24XIV3UWA67UKDAJLFWX/bundle.json","state":"https://pith.science/pith/NJINKD24XIV3UWA67UKDAJLFWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJINKD24XIV3UWA67UKDAJLFWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NJINKD24XIV3UWA67UKDAJLFWX","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":"b1048a6577bcc16e92f7e7c41a4857769794f294d20f4185a0378bc6cfddfac1","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-01T15:01:01Z","title_canon_sha256":"d40bd8b8bc507c63764718ce12e8dfa95c9625c972ec24cc0c129906683e9494"},"schema_version":"1.0","source":{"id":"2204.00502","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.00502","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"arxiv_version","alias_value":"2204.00502v2","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00502","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_12","alias_value":"NJINKD24XIV3","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_16","alias_value":"NJINKD24XIV3UWA6","created_at":"2026-07-05T04:55:51Z"},{"alias_kind":"pith_short_8","alias_value":"NJINKD24","created_at":"2026-07-05T04:55:51Z"}],"graph_snapshots":[{"event_id":"sha256:873a08f444a8d67ef6a6f69cb8f73224944226e6648878ebb4e1182df0096a00","target":"graph","created_at":"2026-07-05T04:55:51Z","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/2204.00502/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence rate of the MD method with strongly convex objective functions in both continuous-time and discrete-time. We formulate the problem of finding convergence rates of the MD algorithms into feasibility problems of linear matrix inequalities (LMIs) in both schemes. In particular, in continuous-time, we show that the Bregman divergence function, which is commonly u","authors_text":"Ioannis Lestas, Khaled Laib, Mengmou Li","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-01T15:01:01Z","title":"Convergence Rate Bounds for the Mirror Descent Method: IQCs and the Bregman Divergence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00502","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":"sha256:53e9d2ebccfe69339cfcce637a97959958bfd197dd7b91fff0650d80f30540b5","target":"record","created_at":"2026-07-05T04:55:51Z","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":"b1048a6577bcc16e92f7e7c41a4857769794f294d20f4185a0378bc6cfddfac1","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-04-01T15:01:01Z","title_canon_sha256":"d40bd8b8bc507c63764718ce12e8dfa95c9625c972ec24cc0c129906683e9494"},"schema_version":"1.0","source":{"id":"2204.00502","kind":"arxiv","version":2}},"canonical_sha256":"6a50d50f5cba2bba581efd14302565b5fbc0d64e2b4f3d2c9346a47dc3949b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a50d50f5cba2bba581efd14302565b5fbc0d64e2b4f3d2c9346a47dc3949b3c","first_computed_at":"2026-07-05T04:55:51.536572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:55:51.536572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w7NgWs9sLFE/iKlRhLg4PgxEqW31nWaDfCbBDRkTZMiiSjCGU4SvGrVGvRySwGSCcJ7F1RfwNnuWZbz7bdGtAg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:55:51.537060Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.00502","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53e9d2ebccfe69339cfcce637a97959958bfd197dd7b91fff0650d80f30540b5","sha256:873a08f444a8d67ef6a6f69cb8f73224944226e6648878ebb4e1182df0096a00"],"state_sha256":"64ff0a3a8d5e0fa8d49f45472a8302d05e6c190830c7110f7c1e7965d48c4ee3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6h4f40a66wEfFj/Mtm8sB/1KvE6LvmFU8nFWnzMeFGL7ccJxHd9JQmByBn+UrzlRooZ3agExN51w0PkgOV8IBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T02:20:50.630805Z","bundle_sha256":"c46ee47d085d8d8f7e1599e0dc41c25f6f842c76258e0646e51b06ecf0e42b0c"}}