Decentralized Resource Allocation via Dual Consensus ADMM

TL;DR

This paper introduces two decentralized algorithms based on ADMM for resource allocation in networked systems, enabling agents to optimize collectively with minimal communication and data sharing, while ensuring convergence.

Contribution

The paper develops two novel dual consensus ADMM methods for decentralized resource allocation with convex conic constraints, proving their convergence and demonstrating effectiveness.

Findings

Methods are fully parallelizable and decentralized.

Algorithms converge under specified conditions.

Numerical example confirms practical effectiveness.

Abstract

We consider a resource allocation problem over an undirected network of agents, where edges of the network define communication links. The goal is to minimize the sum of agent-specific convex objective functions, while the agents' decisions are coupled via a convex conic constraint. We derive two methods by applying the alternating direction method of multipliers (ADMM) for decentralized consensus optimization to the dual of our resource allocation problem. Both methods are fully parallelizable and decentralized in the sense that each agent exchanges information only with its neighbors in the network and requires only its own data for updating its decision. We prove convergence of the proposed methods and demonstrate their effectiveness with a numerical example.