Distributed ADMM with linear updates over directed networks

TL;DR

This paper introduces a distributed ADMM algorithm with linear updates for directed networks, achieving geometric convergence under smooth, strongly convex objectives, and demonstrating improved performance over existing methods.

Contribution

The paper presents a novel distributed ADMM algorithm with linear updates that converges geometrically on directed networks without requiring exact consensus.

Findings

Achieves geometric convergence rate for smooth, strongly convex functions.

Outperforms existing ADMM methods in directed network scenarios.

Demonstrated effectiveness through numerical experiments.

Abstract

We propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our distributed ADMM algorithm achieves a geometric rate of convergence to the optimal point. Our algorithm exploits the robustness inherent to ADMM by not enforcing accurate consensus, thereby significantly improving the convergence rate. We illustrate this by numerical examples, where we compare the performance of our algorithm with that of state-of-the-art ADMM methods over directed graphs.