Distributed generalized Nash equilibrium computing based on dynamic tracking mechanism for nonsmooth aggregative games over time-varying networks

This paper investigates the computation of generalized Nash equilibrium in aggregative games with coupling constraints over time-varying networks. The player’s cost objective comprises a differentiable function dependent on the aggregate of all players’ decisions and a possibly non-smooth term with a linear mapping. In this context, designing solution methods for such game formulation is relatively scarce. We thus develop a fully distributed equilibrium-seeking algorithm that accommodates time-varying communication networks while circumventing the need for global decision information. The proposed algorithm synergistically embeds dynamic tracking of aggregate decisions through a consensus-based mechanism with projected pseudo-gradient updates, augmented by a proximal splitting scheme to handle non-smooth components. Theoretically, we establish convergence guarantees to the variational equilibrium through a new operator splitting framework. Finally, numerical experiments are conducted to substantiate the validity of the proposed algorithm.