  We consider cooperative multi-agent consensus optimization 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 over agent-specific private conic constraint sets;
hence, the optimal consensus decision should lie in the intersection of these
private sets. We provide convergence rates both in sub-optimality,
infeasibility and consensus violation; examine the effect of underlying network
topology on the convergence rates of the proposed decentralized algorithms; and
show how to extend these methods to handle time-varying communications networks
and to solve problems with resource sharing constraints.
