  We present and analyze a computational hybrid architecture for performing
multi-agent optimization. The optimization problems under consideration have
convex objective and constraint functions with mild smoothness conditions
imposed on them. For such problems, we provide a primal-dual algorithm
implemented in the hybrid architecture, which consists of a decentralized
network of agents into which centralized information is occasionally injected,
and we establish its convergence properties. To accomplish this, a central
cloud computer aggregates global information, carries out computations of the
dual variables based on this information, and then distributes the updated dual
variables to the agents. The agents update their (primal) state variables and
also communicate among themselves with each agent sharing and receiving state
information with some number of its neighbors. Throughout, communications with
the cloud are not assumed to be synchronous or instantaneous, and communication
delays are explicitly accounted for in the modeling and analysis of the system.
Experimental results are presented to support the theoretical developments
made.
