On identifying sparse representations of consensus networks*

We consider the problem of identifying optimal sparse graph representations of dense consensus networks. The performance of the sparse representation is characterized by the global performance measure which quantifies the difference between the output of the sparse graph and the output of the original graph. By minimizing the sum of this performance measure and a sparsity-promoting penalty function, the alternating direction method of multipliers identifies sparsity structures that strike a balance between the performance measure and the number of edges in the graph. We then optimize the edge weights of sparse graphs over the identified topologies. Two examples are provided to illustrate the utility of the developed approach.