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In this paper, we focus on solving a distributed convex optimization problemin a network, where each agent has its own convex cost function and the goal isto minimize the sum of the agents' cost functions while obeying the networkconnectivity structure. In order to minimize the sum of the cost functions, weconsider a new distributed gradient-based method where each node maintains twoestimates, namely, an estimate of the optimal decision variable and an estimateof the gradient for the average of the agents' objective functions. From theviewpoint of an agent, the information about the decision variable is pushed tothe neighbors, while the information about the gradients is pulled from theneighbors (hence giving the name "push-pull gradient method"). The methodunifies the algorithms with different types of distributed architecture,including decentralized (peer-to-peer), centralized (master-slave), andsemi-centralized (leader-follower) architecture. We show that the algorithmconverges linearly for strongly convex and smooth objective functions over adirected static network. In our numerical test, the algorithm performs welleven for time-varying directed networks.

A Push-Pull Gradient Method for Distributed Optimization in Networks