Distributed Weight Selection in Consensus Protocols by Schatten Norm Minimization

In this work we study the weight optimization problem for average consensus protocols by reformulating it as a Schatten norm minimization with parameter p. We show that as p approaches infinity, the optimal solution of the Schatten norm induced problem recovers the optimal solution of the original problem. Moreover, by tuning the parameter p in our proposed minimization, we can simply trade-off the quality of the solution (i.e., the speed of convergence) for communication/computation requirements (in terms of number of messages exchanged and volume of data processed). We then propose a distributed algorithm to solve the Schatten norm minimization and we show that it outperforms the other distributed weight selection methods.