  We consider a convex unconstrained optimization problem that arises in a
network of agents whose goal is to cooperatively optimize the sum of the
individual agent objective functions through local computations and
communications. For this problem, we use averaging algorithms to develop
distributed subgradient methods that can operate over a time-varying topology.
Our focus is on the convergence rate of these methods and the degradation in
performance when only quantized information is available. Based on our recent
results on the convergence time of distributed averaging algorithms, we derive
improved upper bounds on the convergence rate of the unquantized subgradient
method. We then propose a distributed subgradient method under the additional
constraint that agents can only store and communicate quantized information,
and we provide bounds on its convergence rate that highlight the dependence on
the number of quantization levels.
