# Projected gradient descent accumulates at Bouligand stationary points

arXiv: https://arxiv.org/abs/2403.02530 · HTML: https://mlsanity.com/paper/2403.02530/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2024.

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

- [Manifold constrained steepest descent for smooth and closed-set optimization](https://mlsanity.com/paper/2601.21487/) (2026)
- [A space-decoupling framework for optimization on bounded-rank matrices with orthogonally invariant constraints](https://mlsanity.com/paper/2501.13830/) (2025)
- [Quantitative Convergence Analysis of Projected Stochastic Gradient Descent for Non-Convex Losses via the Goldstein Subdifferential](https://mlsanity.com/paper/2510.02735/) (2025)

## Abstract (arXiv)

This paper considers the projected gradient descent (PGD) algorithm for the problem of minimizing a continuously differentiable function on a nonempty closed subset of a Euclidean vector space. Without further assumptions, this problem is intractable and algorithms are only expected to find a stationary point. PGD generates a sequence in the set whose accumulation points are known to be Mordukhovich stationary. In this paper, these accumulation points are proven to be Bouligand stationary, and even proximally stationary if the gradient is locally Lipschitz continuous. These are the strongest stationarity properties that can be expected for the considered problem.