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arXiv · 2505.11259

Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes

Gabriele Iommazzo·David Martínez-Rubio·Francisco Criado·Elias Wirth·Sebastian Pokutta
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Abstract

We study the linear convergence of Frank-Wolfe algorithms over product polytopes. We analyze two condition numbers for the product polytope, namely the \emph{pyramidal width} and the \emph{vertex-facet distance}, based on the condition numbers of individual polytope components. As a result, for convex objectives that are $\mu$-Polyak-{\L}ojasiewicz, we show linear convergence rates quantified in terms of the resulting condition numbers. We apply our results to the problem of approximately finding a feasible point in a polytope intersection in high-dimensions, and demonstrate the practical efficiency of our algorithms through empirical results.

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Gabriele Iommazzo, David Martínez-Rubio, Francisco Criado, Elias Wirth, Sebastian Pokutta. 2025-05-16. Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes. https://arxiv.org/abs/2505.11259

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