Distributed Network Flow to Solve Constrained Linear Matrix Equation

In this paper, a novel network flow is presented from a distributed perspective, which aims to solve classical Stein equation. With the coefficient matrices of appropriate dimensions, each agent only access to several row information. That is to say, a standard decomposition method is presented extensively, and then a distributed optimization problem to search least squares solution is proposed by introducing substitutive variables. We show the equivalence between solutions of distributed optimization problem and least squares solution of original Stein equation. Related convex analysis results show that the state solutions of the designed distributed network flow converge to the least squares solution of Stein equation. Finally, numerical results provide the viability of the designed distributed network flow.