Distributed least square approach for solving a multiagent linear algebraic equation

This paper considers a linear algebraic equation over a multiagent network. The coefficient matrix is partitioned into multiple blocks; each agent only knows a subset of these blocks in different row and column partitions. Based on a proximal ADMM algorithm, we design a distributed method for every agent to find its corresponding parts in one least square solution of the considered linear algebraic equation. In every iteration of the designed method, each agent uses only its information and communicates with its neighbors. We show that the designed method achieves an exponentially fast convergence for an arbitrarily initial setup. Numerical simulations in MATLAB are provided to verify the effectiveness of the designed method.