{"paper":{"title":"Convergence Analysis of the Frank-Wolfe Algorithm and Its Generalization in Banach Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hong-Kun Xu","submitted_at":"2017-10-19T23:02:45Z","abstract_excerpt":"The Frank-Wolfe algorithm, a very first optimization method and also known as the conditional gradient method, was introduced by Frank and Wolfe in 1956. Due to its simple linear subproblems, the Frank-Wolfe algorithm has recently been received much attention for solving large-scale structured optimization problems arising from many applied areas such as signal processing and machine learning. In this paper we will discuss in detail the convergence analysis of the Frank-Wolfe algorithm in Banach spaces. Two ways of the selections of the stepsizes are discussed: the line minimization search met"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07367","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":""},"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"}