  We consider cooperative multi-agent resource sharing problems over
time-varying communication networks, where only local communications are
allowed. The objective is to minimize the sum of agent-specific composite
convex functions subject to a conic constraint that couples agents' decisions.
We propose a distributed primal-dual algorithm DPDA-D to solve the saddle point
formulation of the sharing problem on time-varying (un)directed communication
networks; and we show that primal-dual iterate sequence converges to a point
defined by a primal optimal solution and a consensual dual price for the
coupling constraint. Furthermore, we provide convergence rates for
suboptimality, infeasibility and consensus violation of agents' dual price
assessments; examine the effect of underlying network topology on the
convergence rates of the proposed decentralized algorithm; and compare DPDA-D
with a centralized method on the basis pursuit denoising and multi-channel
power allocation problems.
