Affine-coupled Distributed Optimization via Distributed Proximal Jacobian ADMM with Quantized Communication

TL;DR

This paper introduces a new distributed optimization algorithm for resource allocation over directed graphs, combining PJ-ADMM with quantized consensus to reduce communication while maintaining convergence.

Contribution

The paper presents a novel distributed algorithm integrating PJ-ADMM with quantized consensus, achieving efficient resource allocation with bounded accuracy over limited communication channels.

Findings

Achieves sublinear convergence to a neighborhood of the optimal solution.

Convergence accuracy is explicitly bounded by the quantization level.

Numerical experiments show competitive performance with improved communication efficiency.

Abstract

This paper investigates distributed resource allocation optimization over directed graphs with limited communication bandwidth. We develop a novel distributed algorithm that integrates the centralized Proximal Jacobian Alternating Direction Method of Multipliers (PJ-ADMM) with a finite-level quantized consensus scheme, enabling nodes to cooperatively solve the optimization in a distributed fashion. Under the assumption of convex objective functions, we establish that the proposed algorithm achieves sublinear convergence to a neighborhood of the optimal solution, with the convergence accuracy explicitly bounded by the quantization level. Numerical experiments validate that the algorithm achieves competitive performance compared to existing approaches while exhibiting communication efficiency.