Distributed generalized Nash equilibrium seeking: A backward-reflected-forward-backward-based algorithm

Abstract

This paper studies non-cooperative games, in which each player’s local objective function depends on its own decisions as well as those of other players. In these games, each player’s local objective function is differentiable, its decision is constrained by a local feasibility constraint, and the decisions of all players are coupled with an equality constraint. By analyzing the variational problem of the games, a distributed generalized Nash equilibrium seeking algorithm with fixed step sizes is developed based on the backward-reflected-forward–backward splitting. Each player performs a backward step followed by a forward–backward step, and the pseudo-gradient is evaluated at a reflection term. Moreover, the convergence of the proposed distributed algorithm is analyzed under standard assumptions using the operator theory and the convex analysis theory. Finally, the simulation results verify the effectiveness of the algorithm and the correctness of the theoretical analysis.