Frank-Wolfe (F-W) methods are a family of constrained optimization algorithms that have received increasing levels of attention due to the reduced computational resources required in solving F-W subproblems: Particularly in high-dimensional settings, for many constraints that arise in applications (e.g., graph denoising, protein interaction prediction, low-rank regression, and recommender system training), Frank-Wolfe subproblems are significantly easier to solve when compared to traditional projection-based subproblems. This talk is about Frank-Wolfe splitting algorithms, which use speed-advantaged F-W subroutines while enforcing multiple constraints simultaneously. The first algorithms in this class, proposed for convex problems, arose in the late 2010s. We will discuss new algorithms, convergence results, and experiments concerning Frank-Wolfe splitting algorithms for nonconvex settings.

A shorter version of this talk was presented in an invited minisymposium on splitting algorithms at the 2026 SIAM Conference on Optimization at the University of Edinburgh, Scotland, UK.

A preprint containing results from the main paper can be found here. If errors or typos are found, please let me know via email or this form.