Distributed Multi-Step Subgradient Algorithm for Constrained Convex Optimization with Undirected Time-Varying Communications

This paper proposes a novel distributed multi-step subgradient method under a common constraint set with switching undirected graphs. In the proposed method, each agent has a state and a momentum variable as the estimate of an optimal solution and the accumulated information of past gradients of neighbor agents. Similar to a momentum term in the classical momentum-based gradient algorithms, the momentum variable works as inertial force and accelerates convergence rate. We show that the states of all agents asymptotically converge to one of the optimal solutions of the convex optimization problem. The simulation results show that the proposed multi-step subgradient algorithm achieves faster convergence than the standard subgradient algorithms.