We consider distributed optimization in random net- works where nodes cooperatively minimize the sum
of their individual convex costs. Existing literature proposes distributed gradient-like methods that are computationally cheap and resilient to link failures, but have slow convergence rates. In this paper, we propose accelerated distributed gradient methods that 1) are resilient to link failures; 2) computationally cheap; and 3) improve convergence rates over other gradient methods. We model the network by a sequence of independent, identically distributed random matrices drawn from the set of symmetric, stochastic matrices with positive diagonals. The net- work is connected on average and the cost functions are convex, differentiable, with Lipschitz continuous and bounded gradients. We design two distributed Nesterov-like gradient methods that modify the D–NG and D–NC methods that we proposed for static networks. We prove their convergence rates in terms of the expected optimality gap at the cost function. Let and be the number of per-node gradient evaluations and per-node communications, respectively. Then the modified D–NG achieves rates and , and the modified D–NC rates and , where is arbitrarily small. For comparison, the standard distributed gradient method cannot do better than and , on the same class of cost functions (even for static networks). Simulation examples illustrate our analytical findings.