# A Note on the Finite Convergence of Alternating Projections

arXiv: https://arxiv.org/abs/2008.06314 · HTML: https://mlsanity.com/paper/2008.06314/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes](https://mlsanity.com/paper/2505.11259/) (2025)

## Abstract (arXiv)

We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality, which until now has been restricted to sets with nonempty intersection. In the special case of a polyhedron and closed half space, our sufficient conditions define the minimum distance between the two sets that is required for alternating projections to converge in a single iteration.