We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the nonconvex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable op- timization properties to the full to obtain an approach that is completely distributed, has a simple implementation at each node, and capitalizes on an optimal gradient method to attain fast con- vergence. We offer a parallel but also an asynchronous flavor, both with theoretical convergence guarantees and iteration complexity analysis. Experimental results establish leading performance. Our algorithms top the accuracy of a comparable state-of-the-art method by one order of magnitude, using one order of magnitude fewer communications. Index Terms—Convex relaxations, distributed algorithms, dis- tributed iterative sensor localization, maximum likelihood estima- tion, nonconvex optimization, wireless sensor networks.