Decentralized Control Methods in Hypergraph Distributed Optimization

We study a distributed optimization problem which uses an undirected, unweighted hypergraph communication from a dynamical system viewpoint. The stability analysis of the dynamical system is conducted with the use of approaches relevant to non linear decentralized control where we also use the hypergraph Laplacian matrix for the decomposition of the dynamical system. Additionally, we present a Laplacian matrix for the case of a directed and weighted hypergraph and we show how this Laplacian matrix is decomposed for the stability analysis of the distributed optimization problem with the specific directed and weighted hypergraph communication structure.