Decentralized Multi-Agent Optimization Based on a Penalty Method

TL;DR

This paper introduces a decentralized penalty method for convex constrained multi-agent optimization, enabling agents to collaboratively solve problems with minimal communication, and proves its convergence under weak assumptions.

Contribution

It presents a novel decentralized penalty approach with a parallel descent splitting method for convex constrained problems, including a specialization for feasibility issues.

Findings

Method converges under weak assumptions

Agents communicate only with nearest neighbors

Applicable to general convex constrained problems

Abstract

We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be implemented in a computational network where each agent sends information only to the nearest neighbours. Convergence of the method is established under rather weak assumptions. We also describe a specialization of the proposed approach to the feasibility problem.