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

## TL;DR

This paper introduces a novel algorithm for non-convex, non-smooth optimization that effectively escapes saddle points, extending previous results from smooth to non-smooth settings.

## Contribution

It provides the first known theoretical results for escaping saddle points in non-smooth optimization using a perturbed proximal descent method.

## Key findings

- First theoretical guarantees for non-smooth saddle point escape
- Algorithm successfully finds local minima in non-smooth problems
- Extends saddle point analysis to non-smooth optimization

## Abstract

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.