{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6H7A4UOO2BRW6T326FX2FZBA4M","short_pith_number":"pith:6H7A4UOO","schema_version":"1.0","canonical_sha256":"f1fe0e51ced0636f4f7af16fa2e420e3090098aba56173b533e12c6561fc085e","source":{"kind":"arxiv","id":"1812.04517","version":2},"attestation_state":"computed","paper":{"title":"Some Analogue of Quadratic Interpolation for a Special Class of Non-Smooth Functionals and One Application to Adaptive Mirror Descent for Constrained Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fedor S. Stonyakin","submitted_at":"2018-12-11T16:16:31Z","abstract_excerpt":"Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a possibility of constructing an analogue of such interpolation in the class of locally Lipschitz quasi-convex functionals with the special conditions of non-smoothness (Lipshitz-continuous subgradient) introduced in this paper. As an application, estimates are obtained for the rate of convergence of the previously proposed adaptive mirror descent method for the pr"},"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":"1812.04517","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-12-11T16:16:31Z","cross_cats_sorted":[],"title_canon_sha256":"0a298d2f20d55141e0b3e1ef46e2cc9202d82113f31aac1c33373376238cd9a8","abstract_canon_sha256":"fdb397fd50f42dd04b337d35149bc803e418e2516c704d31a207707adf75fdc1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:13.279814Z","signature_b64":"8y/yG+Xrz9bXSM0oasfLpdISdyXUqk7lKQR+kjKkvxsI0inJCk+ulZUbwqRxdjtcymgNpe/N6A9+tHuVltUQDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1fe0e51ced0636f4f7af16fa2e420e3090098aba56173b533e12c6561fc085e","last_reissued_at":"2026-05-17T23:58:13.279134Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:13.279134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some Analogue of Quadratic Interpolation for a Special Class of Non-Smooth Functionals and One Application to Adaptive Mirror Descent for Constrained Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fedor S. Stonyakin","submitted_at":"2018-12-11T16:16:31Z","abstract_excerpt":"Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a possibility of constructing an analogue of such interpolation in the class of locally Lipschitz quasi-convex functionals with the special conditions of non-smoothness (Lipshitz-continuous subgradient) introduced in this paper. As an application, estimates are obtained for the rate of convergence of the previously proposed adaptive mirror descent method for the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04517","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":"1812.04517","created_at":"2026-05-17T23:58:13.279241+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.04517v2","created_at":"2026-05-17T23:58:13.279241+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04517","created_at":"2026-05-17T23:58:13.279241+00:00"},{"alias_kind":"pith_short_12","alias_value":"6H7A4UOO2BRW","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6H7A4UOO2BRW6T32","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6H7A4UOO","created_at":"2026-05-18T12:32:08.215937+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M","json":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M.json","graph_json":"https://pith.science/api/pith-number/6H7A4UOO2BRW6T326FX2FZBA4M/graph.json","events_json":"https://pith.science/api/pith-number/6H7A4UOO2BRW6T326FX2FZBA4M/events.json","paper":"https://pith.science/paper/6H7A4UOO"},"agent_actions":{"view_html":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M","download_json":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M.json","view_paper":"https://pith.science/paper/6H7A4UOO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.04517&json=true","fetch_graph":"https://pith.science/api/pith-number/6H7A4UOO2BRW6T326FX2FZBA4M/graph.json","fetch_events":"https://pith.science/api/pith-number/6H7A4UOO2BRW6T326FX2FZBA4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M/action/storage_attestation","attest_author":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M/action/author_attestation","sign_citation":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M/action/citation_signature","submit_replication":"https://pith.science/pith/6H7A4UOO2BRW6T326FX2FZBA4M/action/replication_record"}},"created_at":"2026-05-17T23:58:13.279241+00:00","updated_at":"2026-05-17T23:58:13.279241+00:00"}