Linear and sublinear convergence rates for a subdifferentiable distributed deterministic asynchronous Dykstra's algorithm

In two earlier papers, we designed a distributed deterministic asynchronous algorithm for minimizing the sum of subdifferentiable and proximable functions and a regularizing quadratic on time-varying graphs based on Dykstra’s algorithm, or block coordinate dual ascent. Each node in the distributed optimization problem is the sum of a known regularizing quadratic and a function to be minimized. In this paper, we prove sublinear convergence rates for the general algorithm, and a linear rate of convergence if the function on each node is smooth with Lipschitz gradient.