{"ID":2891225,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.17272","arxiv_id":"2507.17272","title":"Frank-Wolfe algorithm for star-convex functions","abstract":"We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of \\emph{star-convex functions}, which retain essential geometric properties despite the lack of convexity. We establish iteration-complexity bounds of $\\mathcal{O}(1/k)$ for both the objective values and the duality gap under star-convexity, using diminishing, Armijo-type, and Lipschitz-based stepsize rules. Notably, the diminishing and Armijo strategies do not require prior knowledge of Lipschitz or curvature constants. These results demonstrate that the Frank-Wolfe method preserves optimal complexity guarantees beyond the convex setting.","short_abstract":"We study the Frank-Wolfe algorithm for minimizing a differentiable function with Lipschitz continuous gradient over a compact convex set. To extend classical complexity bounds to certain non-convex functions, we focus on the class of \\emph{star-convex functions}, which retain essential geometric properties despite the...","url_abs":"https://arxiv.org/abs/2507.17272","url_pdf":"https://arxiv.org/pdf/2507.17272v1","authors":"[\"R. Diaz Millan\",\"Orizon Pereira Ferreira\",\"Julien Ugon\"]","published":"2025-07-23T07:18:47Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}