  We present a hybrid systems framework for multi-agent optimization in which
agents execute computations in continuous time and communicate in discrete
time. The optimization algorithm is a continuous-time form of parallelized
coordinate descent. Agents implement a sample-and-hold strategy in which
gradients are computed at communication times and held constant during flows
between communications. The completeness of solutions under these hybrid
dynamics is established. Then, we prove that, under assumptions of smoothness
and strong convexity, this system is globally exponentially stable to the
minimizer of an objective function. Simulation results are presented that
illustrate this convergence rate and the impact of initial conditions upon
convergence.
