AbstractIn this paper we propose a distributed algorithm for solving separable convex optimization problems on graphs arising for example from estimation and control in networks. We derive a primal-dual decomposition algorithm for solving this type of separable optimization problems in a distributed fashion given restrictions on the communication topology. The proposed algorithm is based on consensus principles in combination with local subgradient updates for the primal-dual variables. The main novelty of our algorithm consists in the way the weights in the consensus process are updated using arguments from optimization theory, while in most of the existing distributed algorithms based on consensus principles the weights have to be tuned.