  We propose an algorithm for distributed optimization over time-varying
communication networks. Our algorithm uses an optimized ratio between the
number of rounds of communication and gradient evaluations to achieve fast
convergence. The iterates converge to the global optimizer at the same rate as
centralized gradient descent when measured in terms of the number of gradient
evaluations while using the minimum number of communications to do so.
Furthermore, the iterates converge at a near-optimal rate when measured in
terms of the number of communication rounds. We compare our algorithm with
several other known algorithms on a distributed target localization problem.
