{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:IWKUK2OFW3IHUCOTHAXESUD43W","short_pith_number":"pith:IWKUK2OF","schema_version":"1.0","canonical_sha256":"45954569c5b6d07a09d3382e49507cdd8d762a340d0324f526c091cc6d8dcee4","source":{"kind":"arxiv","id":"1705.03615","version":2},"attestation_state":"computed","paper":{"title":"Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alejandro Ribeiro, Mahyar Fazlyab, Manfred Morari, Victor M. Preciado","submitted_at":"2017-05-10T06:29:34Z","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.03615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-10T06:29:34Z","cross_cats_sorted":[],"title_canon_sha256":"53d1ab8c59aa1caed3cbd167b4967d11543376c34a120b72bbcdef003d54d9af","abstract_canon_sha256":"b864a7c79d0e814ff11419b4b54d3aaaa3016f13da0c45cb19cf92459c75a1f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:44.739627Z","signature_b64":"gUGiv/0VP6CPE+BJl4AGZePMcHcsxDR2oHrILNCIejEFhAY1ZkO8ye7yXKFZMxfGM/FAfGM1UGTPA8Tzyd8FBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45954569c5b6d07a09d3382e49507cdd8d762a340d0324f526c091cc6d8dcee4","last_reissued_at":"2026-05-18T00:22:44.739095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:44.739095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analysis of Optimization Algorithms via Integral Quadratic Constraints: Nonstrongly Convex Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Alejandro Ribeiro, Mahyar Fazlyab, Manfred Morari, Victor M. Preciado","submitted_at":"2017-05-10T06:29:34Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03615","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.03615","created_at":"2026-05-18T00:22:44.739169+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.03615v2","created_at":"2026-05-18T00:22:44.739169+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03615","created_at":"2026-05-18T00:22:44.739169+00:00"},{"alias_kind":"pith_short_12","alias_value":"IWKUK2OFW3IH","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_16","alias_value":"IWKUK2OFW3IHUCOT","created_at":"2026-05-18T12:31:21.493067+00:00"},{"alias_kind":"pith_short_8","alias_value":"IWKUK2OF","created_at":"2026-05-18T12:31:21.493067+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2003.00295","citing_title":"Adaptive Federated Optimization","ref_index":83,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W","json":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W.json","graph_json":"https://pith.science/api/pith-number/IWKUK2OFW3IHUCOTHAXESUD43W/graph.json","events_json":"https://pith.science/api/pith-number/IWKUK2OFW3IHUCOTHAXESUD43W/events.json","paper":"https://pith.science/paper/IWKUK2OF"},"agent_actions":{"view_html":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W","download_json":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W.json","view_paper":"https://pith.science/paper/IWKUK2OF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.03615&json=true","fetch_graph":"https://pith.science/api/pith-number/IWKUK2OFW3IHUCOTHAXESUD43W/graph.json","fetch_events":"https://pith.science/api/pith-number/IWKUK2OFW3IHUCOTHAXESUD43W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W/action/storage_attestation","attest_author":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W/action/author_attestation","sign_citation":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W/action/citation_signature","submit_replication":"https://pith.science/pith/IWKUK2OFW3IHUCOTHAXESUD43W/action/replication_record"}},"created_at":"2026-05-18T00:22:44.739169+00:00","updated_at":"2026-05-18T00:22:44.739169+00:00"}