A geometrically converging dual method for distributed optimization over time-varying graphs

In this paper we consider a distributed convex optimization problem over time-varying undirected networks. We propose a dual method, primarily averaged network dual ascent (PANDA), that is proven to converge R-linearly to the optimal point given that the agents objective functions are strongly convex and have Lipschitz continuous gradients. Like dual decomposition, PANDA requires half the amount of variable exchanges per iterate of methods based on DIGing, and can provide with practical improved performance as empirically demonstrated.Comment: Submitted to Transactions on Automatic Contro

Accelerated Multi-Agent Optimization Method over Stochastic Networks

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of $\mathcal{O}(1/k^2)$. Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.Comment: to appear at the 59th Conference on Decision and Contro

Distributed Augmented Lagrangian Method for Link-Based Resource Sharing Problems of Multi-Agent Systems

A multi-agent optimization problem motivated by the management of energy systems is discussed. The associated cost function is separable and convex although not necessarily strongly convex and there exist edge-based coupling equality constraints. In this regard, we propose a distributed algorithm based on solving the dual of the augmented problem. Furthermore, we consider that the communication network might be time-varying and the algorithm might be carried out asynchronously. The time-varying nature and the asynchronicity are modeled as random processes. Then, we show the convergence and the convergence rate of the proposed algorithm under the aforementioned conditions.Comment: 9 page