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arXiv · 2103.02271

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

Xia Jiang·Xianlin Zeng·Jian Sun·Jie Chen
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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 $O(1/T)$. Finally, we verify the efficacy of proposed algorithm by numerical simulations.

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Xia Jiang, Xianlin Zeng, Jian Sun, Jie Chen. 2021-03-03. Distributed proximal gradient algorithm for non-smooth non-convex optimization over time-varying networks. https://arxiv.org/abs/2103.02271

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