A simple peer-to-peer algorithm for distributed optimization in sensor networks

We propose a distributed algorithm that solves a special class of optimization problems using only peer-to- peer communication. One application is parameter estimation problems in sensor networks. Current decentralized algorithms for solving this class of optimization problems typically rely on passing around a parameter estimate in a ring consisting of all network nodes. In our algorithm, which extends the randomized incremental subgradient method with fixed stepsize due to Nedic and Bertsekas, nodes maintain individual estimates and need to exchange information only with their neighbors. We establish approach of the solution to an interval around the optimum value. We illustrate the algorithm's performance, in terms of convergence rate and communication cost relative to alternative schemes, through several numerical examples.