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.

在本文中，研究了非光滑聚合博弈，其中每个参与者的不可微成本函数取决于其自己的决策以及所有参与者决策的总和。而且，在问题中，参与者的局部约束是一般和异构的凸集，参与者的决策通过线性约束耦合。为了对博弈的变分广义纳什均衡（GNE）进行分布式搜索，开发了一种分布式算法供玩家使用。在算法中，动态平均共识用于估计决策的聚合，以获得近似值成本函数的次梯度。此外，分析了算法对变分GNE的收敛性。最后，仿真实例说明了算法。