A Novel Distributed Algorithm to Seek GNE for Aggregative Games via Primal-Dual Proximal Gradient

In this paper, the generalized Nash equilibria (GNE) problems over the aggregative game is concerned inspired by the widely application of non-cooperative game in many fields. In the game, each agent aims to minimize its own objective function that depends on both its private decision and the average decision information of all agents'. Furthermore, decision variables are within feasible decision sets and shares a global coupling inequality constraint. To seek the GNE, a novel distributed primal-dual proximal algorithm is proposed. Meanwhile, the proposed algorithm adopts edge-based communication model and takes uncoordinated step-sizes that avoid the conservativeness. By the theories of monotone inclusion and averaged operators, convergence of the algorithm is proved. Finally, numerical studies on electric vehicles path and destination strategy problem are conducted to clarify the efficiency of the proposed algorithm.