Distributed least square solution method to linear algebraic equations over multiagent networks

TL;DR

This paper introduces a distributed algorithm based on proximal ADMM for multiagent networks to collaboratively solve linear algebraic equations in a least squares sense, with each agent only using local information and neighbor communication.

Contribution

It proposes a novel discrete-time distributed least squares solution method for linear equations over multiagent networks using proximal ADMM, enabling decentralized computation.

Findings

Method is effective as verified by MATLAB simulations.

Agents can find their parts of the least squares solution using local info.

Communication is limited to neighboring agents, ensuring decentralization.

Abstract

This paper designs a distributed least square solution method for a linear algebraic equation over a multiagent network. The coefficient matrix is divided into multiple blocks, and each agent only knows a subset of these blocks. The designed method is discrete-time and based on a proximal ADMM algorithm. By applying the designed method, each agent can find its corresponding part in one least square solution of the considered linear algebraic equation while using only its information and communicating with its neighbors. Numerical simulations verify the effectiveness of the designed method in MATLAB.