Multi-agent constrained optimization of a strongly convex function over time-varying directed networks

We consider cooperative multi-agent consensus optimization problems over undirected and directed time-varying communication networks, where only local communications are allowed. The objective is to minimize the sum of agent-specific possibly non-smooth composite convex functions over agent-specific private conic constraint sets; hence, the optimal consensus decision should lie in the intersection of these private sets. Assuming the sum function is strongly convex, we provide convergence rates in sub-optimality, infeasibility and consensus violation; examine the effect of underlying network topology on the convergence rates of the proposed decentralized algorithm.