Distributed Alternating Direction Method of Multipliers for Linearly Constrained Optimization Over a Network

Abstract

In this letter we address the distributed optimization problem for a network of agents, which commonly occurs in several control engineering applications. Differently from the related literature, where only consensus constraints are typically addressed, we consider a challenging distributed optimization set-up where agents rely on local communication and computation to optimize a sum of local objective functions, each depending on individual variables subject to local constraints, while satisfying linear coupling constraints. Thanks to the distributed scheme, the resolution of the optimization problem turns into designing an iterative control procedure that steers the strategies of agents-whose dynamics is decoupled-not only to be convergent to the optimal value but also to satisfy the coupling constraints. Based on duality and consensus theory, we develop a proximal Jacobian alternating direction method of multipliers (ADMM) for solving such a kind of linearly constrained convex optimization problems over a network. Using the monotone operator and fixed point mapping, we analyze the optimality of the proposed algorithm and establish its o(1/t) convergence rate. Finally, through numerical simulations we show that the proposed algorithm offers higher computational performances than recent distributed ADMM variants.