Distributed generalized Nash equilibrium seeking algorithm for nonsmooth aggregative games

In this paper, nonsmooth aggregative games are investigated, where the nondifferentiable cost function of every player depends on its own decision as well as the aggregate of the decisions of all players. Moreover, in the problem, the local constraints of players are general and heterogeneous convex sets, and the decisions of players are coupled by linear constraints. For purpose of distributed seeking of the variational generalized Nash equilibrium (GNE) of the game, a distributed algorithm is developed for players. In the algorithm, the dynamic average consensus is used for the estimation of the aggregate of decisions to obtain the approximation of subgradients of cost functions. Besides, the convergence of the algorithm to the variational GNE is analyzed. Finally, simulation examples illustrate the algorithm.