Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks
Abstract
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 . Finally, we verify the efficacy of proposed algorithm by numerical simulations.
Cite
@article{arxiv.2103.02271,
title = {Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks},
author = {Xia Jiang and Xianlin Zeng and Jian Sun and Jie Chen},
journal= {arXiv preprint arXiv:2103.02271},
year = {2021}
}