A Distributed Parallel Optimization Algorithm via Alternating Direction Method of Multipliers

TL;DR

This paper introduces a new distributed parallel ADMM algorithm enabling agents to update local states and dual variables concurrently, ensuring convergence to the optimal solution with a rate of O(1/k).

Contribution

It proposes a modified distributed parallel ADMM that allows fully distributed and parallel updates, improving efficiency over existing sequential methods.

Findings

Agents reach consensus asymptotically.

Global cost function converges to optimal value at rate O(1/k).

Simulation confirms effectiveness of the algorithm.

Abstract

Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to update their local states and dual variables in a completely distributed and parallel manner by modifying the existing distributed sequential ADMM. Moreover, the updating rules and storage method for variables are illustrated. It is shown that all the agents can reach a consensus by asymptotically converging to the optimal solution. Besides, the global cost function will converge to the optimal value at a rate of O(1/k). Simulation results on a numerical example are given to show the effectiveness of the proposed algorithm.