{"paper":{"title":"Frank-Wolfe Algorithms for (L0, L1)-smooth functions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A new Frank-Wolfe algorithm for (L0, L1)-smooth objectives achieves superior convergence rates.","cross_cats":[],"primary_cat":"math.OC","authors_text":"A.A. Vyguzov, F.S. Stonyakin","submitted_at":"2025-10-18T12:26:28Z","abstract_excerpt":"We propose a new version of the Frank-Wolfe method, called the (L0, L1)-Frank-Wolfe algorithm, developed for optimization problems with (L0, L1)-smooth objectives. We establish that this algorithm achieves superior theoretical convergence rates compared to the classical Frank-Wolfe method. In addition, we introduce a novel adaptive procedure, termed the Adaptive (L0, L1)-Frank-Wolfe algorithm, which dynamically adjusts the smoothness parameters to further improve performance and stability. Comprehensive numerical experiments confirm the theoretical results and demonstrate the clear practical a"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish that this algorithm achieves superior theoretical convergence rates compared to the classical Frank-Wolfe method.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The objective functions satisfy the (L0, L1)-smoothness condition that the new algorithm is designed to exploit for its improved rates (as stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new (L0, L1)-Frank-Wolfe algorithm and its adaptive version are proposed for (L0, L1)-smooth optimization, with claims of better theoretical convergence rates and practical advantages over standard Frank-Wolfe methods.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A new Frank-Wolfe algorithm for (L0, L1)-smooth objectives achieves superior convergence rates.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f69488c153b3381d1262d104e41cb24dd5f3c7a03104f40775dde4e564f9e371"},"source":{"id":"2510.16468","kind":"arxiv","version":4},"verdict":{"id":"cfd172e3-73aa-42bf-a8b3-266c147a7798","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T06:15:35.242813Z","strongest_claim":"We establish that this algorithm achieves superior theoretical convergence rates compared to the classical Frank-Wolfe method.","one_line_summary":"A new (L0, L1)-Frank-Wolfe algorithm and its adaptive version are proposed for (L0, L1)-smooth optimization, with claims of better theoretical convergence rates and practical advantages over standard Frank-Wolfe methods.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The objective functions satisfy the (L0, L1)-smoothness condition that the new algorithm is designed to exploit for its improved rates (as stated in the abstract).","pith_extraction_headline":"A new Frank-Wolfe algorithm for (L0, L1)-smooth objectives achieves superior convergence rates."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.16468/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":2,"snapshot_sha256":"f6aae87b4addc9041ad5739415c2be3cd33ab177968fcf0a87322f24fdeb2c43"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}