Distributed dual averaging method for solving saddle-point problems over multi-agent networks

In this paper we study the multi-agent saddle-point problems where multiple agents try to collectively optimize a sum of local convex-concave functions, each of which is available to one specific agent in the network. We propose a distributed primal-dual subgradient method, by using the dual averaging method in combination with an average consensus process. The method can be implemented over a time-varying network while satisfying some standard connectivity conditions. We provide convergence results and convergence rate estimates for the proposed method.