2021/03/03 by Jiang, Xia, Zeng, Xianlin, Sun, Jian +1
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2103.02271
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.