{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IWKUK2OFW3IHUCOTHAXESUD43W","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":"b864a7c79d0e814ff11419b4b54d3aaaa3016f13da0c45cb19cf92459c75a1f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-10T06:29:34Z","title_canon_sha256":"53d1ab8c59aa1caed3cbd167b4967d11543376c34a120b72bbcdef003d54d9af"},"schema_version":"1.0","source":{"id":"1705.03615","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03615","created_at":"2026-05-18T00:22:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03615v2","created_at":"2026-05-18T00:22:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03615","created_at":"2026-05-18T00:22:44Z"},{"alias_kind":"pith_short_12","alias_value":"IWKUK2OFW3IH","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IWKUK2OFW3IHUCOT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IWKUK2OF","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:269b54b03f494c522db537ebc18e151afb6bb807996bf0fa3260bc2692510295","target":"graph","created_at":"2026-05-18T00:22:44Z","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 develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent nonquadratic Lyapunov functions that can generate convergence rates in addition to proving asymptotic convergence. Using Integral Quadratic Constraints (IQCs) from robust control theory, we propose a Linear Matrix Inequality (LMI) to guide the search for the parameters of the Lyapunov function in order to establish a rate bound. Based on this result, we for","authors_text":"Alejandro Ribeiro, Mahyar Fazlyab, Manfred Morari, Victor M. Preciado","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-10T06:29:34Z","title":"Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03615","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:f7c7da0b0120bec4b643fe56ae75b3ff8eefe032787ea0c580a804859af8734a","target":"record","created_at":"2026-05-18T00:22:44Z","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":"b864a7c79d0e814ff11419b4b54d3aaaa3016f13da0c45cb19cf92459c75a1f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-10T06:29:34Z","title_canon_sha256":"53d1ab8c59aa1caed3cbd167b4967d11543376c34a120b72bbcdef003d54d9af"},"schema_version":"1.0","source":{"id":"1705.03615","kind":"arxiv","version":2}},"canonical_sha256":"45954569c5b6d07a09d3382e49507cdd8d762a340d0324f526c091cc6d8dcee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45954569c5b6d07a09d3382e49507cdd8d762a340d0324f526c091cc6d8dcee4","first_computed_at":"2026-05-18T00:22:44.739095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:44.739095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gUGiv/0VP6CPE+BJl4AGZePMcHcsxDR2oHrILNCIejEFhAY1ZkO8ye7yXKFZMxfGM/FAfGM1UGTPA8Tzyd8FBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:44.739627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03615","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7c7da0b0120bec4b643fe56ae75b3ff8eefe032787ea0c580a804859af8734a","sha256:269b54b03f494c522db537ebc18e151afb6bb807996bf0fa3260bc2692510295"],"state_sha256":"0ac374e1b445e983098b558a4c4199c32302908516d125f23e99b4d03e0974f6"}