A distributed parallel optimization algorithm via alternating direction method of multipliers

Alternating direction method of multipliers (ADMM) has been widely used for solving the distributed optimisation problems. This paper proposes a novel distributed ADMM algorithm to solve the distributed optimisation problems consisting of convex cost functions under an undirected connected graph. The proposed algorithm adopts the concepts of predecessors and successors in the distributed sequential ADMM algorithm, but changes the sequential updating manner to a parallel one, which allows the agents to update their local states and dual variables in a completely distributed and parallel manner. This brings some benefits when solving large‐scale optimisation problems. Variational inequality is applied to analyse the convergence of agents' states. It is proved that the states of all the agents converge to the optimal point, and the global cost function converge to the optimal value at a rate of O(1/k)$O(1/k)$. Numerical experiments are given to show the effectiveness and suitability of the proposed algorithm. This article proposes a novel alternating direction method of multipliers‐based distributed optimisation algorithm. This algorithm holds an evolution of ergodic convergence into state convergence. The proposed algorithm shows a competitive convergence rate compared with algorithms of the same type.