Momentum-based Distributed Generalized Nash Equilibrium Seeking in Merely Monotone Games

This paper is concerned with distributed generalized Nash equilibrium (GNE) seeking problem for noncooperative monotone games with coupled constraints. Each individual player aims to minimize its local cost function, which depends not only on its own decision, but also on other players’ decisions. By exploiting variational equilibrium as a solution and operator splitting, the problem is restated as seeking the zero of monotone operators. Then, we first propose a novel distributed GNE seeking algorithm based on the modified version of forward–reflected-backward splitting with the incorporation of a Nesterov’s momentum technique, which is shown to be convergent under monotone and Lipschitz conditions on the pseudo-gradient mapping. Compared with the literature, it improves the convergence performance and relaxes monotonicity and cocoercivity assumptions. Finally, numerical experiments are presented to illustrate the validity of the distributed algorithm.