Distributed algorithm for solving variational inequalities over time-varying unbalanced digraphs

In this paper, we study a distributed model to cooperatively compute variational inequalities over time-varying directed graphs. Here, each agent has access to a part of the full mapping and holds a local view of the global set constraint. By virtue of an auxiliary vector to compensate the graph imbalance, we propose a consensus-based distributed projection algorithm relying on local computation and communication at each agent. We show the convergence of this algorithm over uniformly jointly strongly connected unbalanced digraphs with nonidentical local constraints. We also provide a numerical example to illustrate the effectiveness of our algorithm.