  We present a framework for asynchronously solving convex optimization
problems over networks of agents which are augmented by the presence of a
centralized cloud computer. This framework uses a Tikhonov-regularized
primal-dual approach in which the agents update the system's primal variables
and the cloud updates its dual variables. To minimize coordination requirements
placed upon the system, the times of communications and computations among the
agents are allowed to be arbitrary, provided they satisfy mild conditions.
Communications from the agents to the cloud are likewise carried out without
any coordination in their timing. However, we require that the cloud keep the
dual variable's value synchronized across the agents, and a counterexample is
provided that demonstrates that this level of synchrony is indeed necessary for
convergence. Convergence rate estimates are provided in both the primal and
dual spaces, and simulation results are presented that demonstrate the
operation and convergence of the proposed algorithm.
