{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:QY4T3JPD4NBRMELINFS6NICYPP","short_pith_number":"pith:QY4T3JPD","schema_version":"1.0","canonical_sha256":"86393da5e3e3431611686965e6a0587be2f992ea07d67670377f79ff3e41669a","source":{"kind":"arxiv","id":"2308.06470","version":1},"attestation_state":"computed","paper":{"title":"On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fan Chen, Junyu Zhang, Zaiwen Wen, Zhenyuan Zhu","submitted_at":"2023-08-12T05:28:05Z","abstract_excerpt":"We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\\min_x\\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly convex, convex, and nonconvex $f$, we design efficient first order algorithms with complexities $\\tilde{O}\\left(\\kappa_A\\sqrt{\\kappa_f}\\log\\left(1/{\\epsilon}\\right)\\right)$, $\\tilde{O}\\left(\\kappa_A\\sqrt{L_f}D/\\sqrt{\\epsilon}\\right)$, and $\\tilde{O}\\left(\\kappa_A L_f\\Delta/\\epsilon^2\\right)$, respectively. Here, $\\kappa_A$ is the condition number of the matrix $"},"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":"2308.06470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-08-12T05:28:05Z","cross_cats_sorted":[],"title_canon_sha256":"a1800938a97f4b29468531b9c43c7889bbb0d2174f9f8e90b69aa64f429defb5","abstract_canon_sha256":"11bef8523f67f58103ea722ad7147a287fd0fb7bb13a7252164548c354dfd2ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:40:40.560106Z","signature_b64":"RK+gnrEptPk+2J1qjWQXNugxVUKYMwep2dkp3jItvLI8Rp0GzMgPK+7YiycznmlY7PF+OA0OzvRfu4NBkFBhDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86393da5e3e3431611686965e6a0587be2f992ea07d67670377f79ff3e41669a","last_reissued_at":"2026-07-05T06:40:40.559598Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:40:40.559598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Optimal Lower and Upper Complexity Bounds for a Class of Composite Optimization Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Fan Chen, Junyu Zhang, Zaiwen Wen, Zhenyuan Zhu","submitted_at":"2023-08-12T05:28:05Z","abstract_excerpt":"We study the optimal lower and upper complexity bounds for finding approximate solutions to the composite problem $\\min_x\\ f(x)+h(Ax-b)$, where $f$ is smooth and $h$ is convex. Given access to the proximal operator of $h$, for strongly convex, convex, and nonconvex $f$, we design efficient first order algorithms with complexities $\\tilde{O}\\left(\\kappa_A\\sqrt{\\kappa_f}\\log\\left(1/{\\epsilon}\\right)\\right)$, $\\tilde{O}\\left(\\kappa_A\\sqrt{L_f}D/\\sqrt{\\epsilon}\\right)$, and $\\tilde{O}\\left(\\kappa_A L_f\\Delta/\\epsilon^2\\right)$, respectively. Here, $\\kappa_A$ is the condition number of the matrix $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.06470","kind":"arxiv","version":1},"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/2308.06470/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2308.06470","created_at":"2026-07-05T06:40:40.559660+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.06470v1","created_at":"2026-07-05T06:40:40.559660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.06470","created_at":"2026-07-05T06:40:40.559660+00:00"},{"alias_kind":"pith_short_12","alias_value":"QY4T3JPD4NBR","created_at":"2026-07-05T06:40:40.559660+00:00"},{"alias_kind":"pith_short_16","alias_value":"QY4T3JPD4NBRMELI","created_at":"2026-07-05T06:40:40.559660+00:00"},{"alias_kind":"pith_short_8","alias_value":"QY4T3JPD","created_at":"2026-07-05T06:40:40.559660+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.19050","citing_title":"First-Order Methods for Solving Convex (Strongly) Concave Minimax Problems with Functional Constraints","ref_index":71,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP","json":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP.json","graph_json":"https://pith.science/api/pith-number/QY4T3JPD4NBRMELINFS6NICYPP/graph.json","events_json":"https://pith.science/api/pith-number/QY4T3JPD4NBRMELINFS6NICYPP/events.json","paper":"https://pith.science/paper/QY4T3JPD"},"agent_actions":{"view_html":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP","download_json":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP.json","view_paper":"https://pith.science/paper/QY4T3JPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.06470&json=true","fetch_graph":"https://pith.science/api/pith-number/QY4T3JPD4NBRMELINFS6NICYPP/graph.json","fetch_events":"https://pith.science/api/pith-number/QY4T3JPD4NBRMELINFS6NICYPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP/action/storage_attestation","attest_author":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP/action/author_attestation","sign_citation":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP/action/citation_signature","submit_replication":"https://pith.science/pith/QY4T3JPD4NBRMELINFS6NICYPP/action/replication_record"}},"created_at":"2026-07-05T06:40:40.559660+00:00","updated_at":"2026-07-05T06:40:40.559660+00:00"}