Parallel alternating direction method of multipliers

In this paper, we consider the distributed optimization problem, where the objective function is the sum of local cost functions. To solve this problem, a new parallel Alternating Direction Method of Multipliers (ADMM) algorithm is developed, which guarantees that the agents cooperatively reach an optimal agreement. Different from most of the existing ADMM approaches, our algorithm allows all the agents to update their local variables simultaneously in a parallel manner. It is theoretically proved that the local solutions of all the agents could reach a consensus, and converge to the optimal solution asymptotically with the rate of O(1/k). Numerical examples are finally provided to validate the effectiveness of the proposed method.