# Perturbed Proximal Descent to Escape Saddle Points for Non-convex and Non-smooth Objective Functions

arXiv: https://arxiv.org/abs/1901.08958 · HTML: https://mlsanity.com/paper/1901.08958/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2019.

## Built on by (most cited first, 4 of 4)

- [Stochastic Gradient Langevin Dynamics with Variance Reduction](https://mlsanity.com/paper/2102.06759/) (2021)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Escaping Saddle Points for Nonsmooth Weakly Convex Functions via Perturbed Proximal Algorithms](https://mlsanity.com/paper/2102.02837/) (2021)
- [Single-pass Object-adaptive Data Undersampling and Reconstruction for MRI](https://mlsanity.com/paper/2111.09212/) (2021)

## Abstract (arXiv)

We consider the problem of finding local minimizers in non-convex and non-smooth optimization. Under the assumption of strict saddle points, positive results have been derived for first-order methods. We present the first known results for the non-smooth case, which requires different analysis and a different algorithm.