  We consider cooperative multi-agent consensus optimization problems over both
static and 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 suboptimality, infeasibility and
consensus violation; examine the effect of underlying network topology on the
convergence rates of the proposed decentralized algorithms.
