Model-distributed solution of regularized least-squares problem over sensor networks

We develop a fully-distributed iterative algorithm for finding a model-distributed least-squares solution of systems of linear equations over sensor networks. Here, model-distributed means the solution vector is distributed across the network rather than being replicated at each node. For this purpose, we devise a dual regularized least-squares problem via a suitable decomposition of the normal equations associated with the original problem. The resultant dual problem can be solved in a fully-decentralized and iterative manner by means of the diffusion-based Pareto optimization strategy. We verify the usefulness of the proposed algorithm via both theoretical analysis and numerical examples.