Solving least-squares problems in directed networks: A distributed approach

Abstract

In this paper, we introduce a distributed algorithm that is specifically designed to tackle the least-squares problem within a network system of linear algebraic equations. Our focus is on static directed multi-agent networks, where each agent possesses knowledge of a distinct subset of the linear equations. Furthermore, we examine a scenario where agents lack information about their “out-degrees” at any given time. By imposing the strong connectivity condition on the communication network, we establish that the local estimated solution of each agent exhibits exponential convergence towards the least-squares solution of the corresponding network system of linear algebraic equations.