Linear Convergence Rate Analysis of a Class of Exact First-Order Distributed Methods for Time-Varying Directed Networks and Uncoordinated Step Sizes

A class of exact first order methods for distributed optimization is considered. Under the standard assumption on the cost function - convexity and Lipschitz continuity of the gradient, we extend the convergence results to the setting of time-varying directed networks and node specific time-varying step sizes. The convergence result is obtained without assuming connectivity of the underlying network in each iteration. Furthermore, node specific step sizes that vary through iterations diminish the need for coordination among different nodes.