Decentralized Alternating Direction Method of Multipliers for Constrained Optimization over Directed Networks

In this paper, we consider the decentralized constrained optimization problem in which the objective is to minimize the sum of convex functions subject to equality and set constraints over a directed network. To tackle the optimization problem, we introduce a new algorithm that integrates finite-time weighted average consensus with the Alternating Direction Method of Multipliers (ADMM). Most decentralized optimization algorithms for solving this problem over directed networks use a column-stochastic weight matrix, which necessitates that each agent be aware of its own out-degree. However, the proposed algorithm eliminates this requirement but uses a row-stochastic weight matrix. Additionally, the provided algorithm is proven to achieve a sublinear convergence rate. Finally, the efficacy of our algorithm is confirmed through the numerical simulations performed on a least squares problem subject to local equality and set constraints.