# Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks

arXiv: https://arxiv.org/abs/2103.02271 · HTML: https://mlsanity.com/paper/2103.02271/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Distributed stochastic proximal algorithm with random reshuffling for non-smooth finite-sum optimization](https://mlsanity.com/paper/2111.03820/) (2021)

## Abstract (arXiv)

This note studies the distributed non-convex optimization problem with non-smooth regularization, which has wide applications in decentralized learning, estimation and control. The objective function is the sum of different local objective functions, which consist of differentiable (possibly non-convex) cost functions and non-smooth convex functions. This paper presents a distributed proximal gradient algorithm for the non-smooth non-convex optimization problem over time-varying multi-agent networks. Each agent updates local variable estimate by the multi-step consensus operator and the proximal operator. We prove that the generated local variables achieve consensus and converge to the set of critical points with convergence rate O(1/T). Finally, we verify the efficacy of proposed algorithm by numerical simulations.