# Euclidean distance degree in manifold optimization

arXiv: https://arxiv.org/abs/2502.10336 · HTML: https://mlsanity.com/paper/2502.10336/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Feb 2025.

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

- [Robustness Verification of Polynomial Neural Networks](https://mlsanity.com/paper/2602.06105/) (2026)

## Abstract (arXiv)

We determine the Euclidean distance degrees of the three most common manifolds arising in manifold optimization: flag, Grassmann, and Stiefel manifolds. For the Grassmannian, we will also determine the Euclidean distance degree of an important class of Schubert varieties that often appear in applications. Our technique goes further than furnishing the value of the Euclidean distance degree; it will also yield closed-form expressions for all stationary points of the Euclidean distance function in each instance. We will discuss the implications of these results on the tractability of manifold optimization problems.