A distributed ADMM-like method for resource sharing over time-varying networks

We consider cooperative multiagent resource sharing problems over time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific composite convex functions subject to a conic constraint that couples agents' decisions. We propose a distributed primal-dual algorithm, DPDA-D, to solve the saddle-point formulation of the sharing problem on time-varying (un)directed communication networks; and we show that the primal-dual iterate sequence converges to a point defined by a primal optimal solution and a consensual dual price for the coupling constraint. Furthermore, we provide convergence rates for suboptimality, infeasibility, and consensus violation of agents' dual price assessments; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm; and compare DPDA-D with centralized methods on the basis pursuit denoising and multichannel power allocation problems.