# Stochastic Proximal Methods for Non-Smooth Non-Convex Constrained Sparse Optimization

arXiv: https://arxiv.org/abs/1905.10188 · HTML: https://mlsanity.com/paper/1905.10188/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

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

- [Fusion of Global and Local Knowledge for Personalized Federated Learning](https://mlsanity.com/paper/2302.11051/) (2023)
- [Stochastic Variable Metric Proximal Gradient with variance reduction for non-convex composite optimization](https://mlsanity.com/paper/2301.00631/) (2023)
- [Outlier-robust neural network training: variation regularization meets trimmed loss to prevent functional breakdown](https://mlsanity.com/paper/2308.02293/) (2023)
- [A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-Lojasiewicz condition](https://mlsanity.com/paper/2608.05460/) (2026)

## Abstract (arXiv)

This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic convergence results for this class of problem. We present two simple stochastic proximal gradient algorithms, for general stochastic and finite-sum optimization problems, which have the same or superior convergence complexities compared to the current best results for the unconstrained problem setting. In a numerical experiment we compare our algorithms with the current state-of-the-art deterministic algorithm and find our algorithms to exhibit superior convergence.