# Transversality and alternating projections for nonconvex sets

arXiv: https://arxiv.org/abs/1401.7569 · HTML: https://mlsanity.com/paper/1401.7569/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2014.

## Built on by (most cited first, 3 of 3)

- [Provable Phase Retrieval with Mirror Descent](https://mlsanity.com/paper/2210.09248/) (2022)
- [Linear Convergence of the Frank-Wolfe Algorithm over Product Polytopes](https://mlsanity.com/paper/2505.11259/) (2025)
- [Optimization over the intersection of manifolds](https://mlsanity.com/paper/2605.22736/) (2026)

## Abstract (arXiv)

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear convergence. When the two sets are semi-algebraic and bounded, but not necessarily transversal, we nonetheless prove subsequence convergence.