{"paper":{"title":"Universal Conditional Gradient Sliding for Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Trevor Squires, Yuyuan Ouyang","submitted_at":"2021-03-19T21:23:18Z","abstract_excerpt":"In this paper, we present a first-order projection-free method, namely, the universal conditional gradient sliding (UCGS) method, for solving $\\varepsilon$-approximate solutions to convex differentiable optimization problems. For objective functions with H\\\"older continuous gradients, we show that UCGS is able to terminate with $\\varepsilon$-solutions with at most $O((M_\\nu D_X^{1+\\nu}/{\\varepsilon})^{2/(1+3\\nu)})$ gradient evaluations and $O((M_\\nu D_X^{1+\\nu}/{\\varepsilon})^{4/(1+3\\nu)})$ linear objective optimizations, where $\\nu\\in (0,1]$ and $M_\\nu>0$ are the exponent and constant of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.11026","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/2103.11026/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"}