Distributed Constrained Optimization with Linear Convergence Rate

This paper considers the consensus optimization problems with identical convex constraint sets, via local computation and communication under an undirected graph. To solve the problem, we propose algorithm combining projection operation, gradient tracking technique and consensus method. With the help of the strong convexity assumption and l-smooth assumption, the proposed algorithm with fixed stepsize is proved to converge linearly to the optimal solution under a connected graph and an assumption on the communication weight matrix. We establish explicit theoretical estimates for the convergence rate. The results are also demostrated by numerical experiments.