# Frank-Wolfe Algorithms for (L0, L1)-smooth functions

arXiv: https://arxiv.org/abs/2510.16468 · HTML: https://mlsanity.com/paper/2510.16468/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2025.

## Built on by (most cited first, 2 of 2)

- [Broximal Gradient Descent: A Projection-Free Sister of Projected Gradient Descent](https://mlsanity.com/paper/2605.08850/) (2026)
- [Polyak-Type Extragradient Methods for Monotone Root-Finding Problems](https://mlsanity.com/paper/2609.26581/) (2026)

## Abstract (arXiv)

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 advantages of both proposed algorithms over existing Frank-Wolfe variants.