Distributed primal-dual method for multi-agent sharing problem with conic constraints

We consider cooperative multi-agent resource sharing problems over an undirected network of agents, where only those agents connected by an edge can directly communicate. The objective is to minimize the sum of agent-specific composite convex functions subject to a conic constraint that couples agents' decisions. A distributed primal-dual algorithm is proposed to solve the saddle point formulation, which requires to compute a consensus dual price for the coupling constraint. We provide convergence rates in sub-optimality, infeasibility and consensus violation for agents' dual price assessments; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm; and compare our method with Prox-JADMM algorithm on the basis pursuit problem.