{"ID":2896887,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.05669","arxiv_id":"2507.05669","title":"A Fully Adaptive Frank-Wolfe Algorithm for Relatively Smooth Problems and Its Application to Centralized Distributed Optimization","abstract":"We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size. Our method does not require prior knowledge of the function parameters and guarantees convergence using only local information. We establish a linear convergence rate under relative strong convexity and provide a detailed theoretical analysis of the proposed adaptive step-size rule. Furthermore, we demonstrate how relative smoothness and strong convexity naturally arise in the setting of centralized distributed optimization. Under a variance-type assumption on the gradients, we show that the global objective becomes relatively strongly convex with respect to the Bregman divergence generated by a local function. This structure allows us to apply our adaptive Frank-Wolfe algorithm, leading to provable acceleration due to an improved relative condition number.","short_abstract":"We study the Frank-Wolfe algorithm for constrained optimization problems with relatively smooth objectives. Building upon our previous work, we propose a fully adaptive variant of the Frank-Wolfe method that dynamically adjusts the step size. Our method does not require prior knowledge of the function parameters and gu...","url_abs":"https://arxiv.org/abs/2507.05669","url_pdf":"https://arxiv.org/pdf/2507.05669v2","authors":"[\"A. A. Vyguzov\",\"F. S. Stonyakin\"]","published":"2025-07-08T04:53:21Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}