A Distributed Network Flow for Nonnegative Least Squares Solutions
Mohammad Jahvani, Martin Guay · IFAC-PapersOnLine · 2021
In this paper, we introduce a distributed continuous-time network flow without using projections for the computation of nonnegative least-squares solution to a linear algebraic equation of the form Ax = b where A has full column rank. It is assumed that each one of the n autonomous agents only knows a subset of the partitioned matrix [A b], and exchanges its local estimate of the optimal solution with certain other agents called its neighbors. Neighbor relations are characterized by a graph G whose vertices correspond to the labels of agents and whose edges depict the neighbor relations. It is shown that for any such matrix A and any connected and undirected neighbor graph, the estimates of all agents in the proposed algorithm asymptotically converge to the desired solution.