  Motivated by applications in machine learning and statistics, we study
distributed optimization problems over a network of processors, where the goal
is to optimize a global objective composed of a sum of local functions. In
these problems, due to the large scale of the data sets, the data and
computation must be distributed over processors resulting in the need for
distributed algorithms. In this paper, we consider a popular distributed
gradient-based consensus algorithm, which only requires local computation and
communication. An important problem in this area is to analyze the convergence
rate of such algorithms in the presence of communication delays that are
inevitable in distributed systems. We prove the convergence of the
gradient-based consensus algorithm in the presence of uniform, but possibly
arbitrarily large, communication delays between the processors. Moreover, we
obtain an upper bound on the rate of convergence of the algorithm as a function
of the network size, topology, and the inter-processor communication delays.
