A decomposition method for a class of convex generalized Nash equilibrium problems

In this paper, we study a numerical approach to compute a solution of the generalized Nash equilibrium problem (GNEP). The GNEP is a potent modeling tool that has been increasingly developing in recent decades. Much of this development has centered around applying variational methods to the so-called GNSC, a useful but restricted subset of GNEP where each player has the same constraint set. One popular approach to solve the GNSC is to use the apparent separability of each player to build a decomposition method. This method has the benefit of being easily implementable and can be parallelized. Our aim in this paper is to show an extension of the decomposition method to a class of convex GNEP. We prove convergence of the proposed algorithm under a full convexity assumption. Then, we show numerical results on some examples to validate our approach and discuss the assumptions.