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We consider cooperative multi-agent consensus optimization problems over bothstatic and time-varying communication networks, where only local communicationsare allowed. The objective is to minimize the sum of agent-specific possiblynon-smooth composite convex functions over agent-specific private conicconstraint sets; hence, the optimal consensus decision should lie in theintersection of these private sets. Assuming the sum function is stronglyconvex, we provide convergence rates in suboptimality, infeasibility andconsensus violation; examine the effect of underlying network topology on theconvergence rates of the proposed decentralized algorithms.

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