# Proximal methods avoid active strict saddles of weakly convex functions

arXiv: https://arxiv.org/abs/1912.07146 · HTML: https://mlsanity.com/paper/1912.07146/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Active manifolds, stratifications, and convergence to local minima in nonsmooth optimization](https://mlsanity.com/paper/2108.11832/) (2021)
- [Escaping Saddle Points for Nonsmooth Weakly Convex Functions via Perturbed Proximal Algorithms](https://mlsanity.com/paper/2102.02837/) (2021)

## Abstract (arXiv)

We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems.