Distributed Generalized Nash Equilibrium Seeking for Monotone Generalized Noncooperative Games by a Regularized Penalized Dynamical System.

In this work, we study the generalized Nash equilibrium (GNE, see Definition 1) seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A novel projected gradient-based regularized penalized dynamical system is proposed to solve this issue. The idea is to use a differentiable penalty function with a time-varying penalty parameter to deal with the inequality constraints. A time-varying regularization term is used to deal with the ill-poseness caused by the monotonicity assumption and the time-varying penalty term. The proposed dynamical system extends the regularized dynamical system in the literature to the projected gradient-based regularized penalized dynamical system, which can be used to solve generalized noncooperative games with set constraints and coupled constraints. Furthermore, we propose a distributed algorithm by using leader-following consensus, where the players have access to neighboring information only. For both cases, the asymptotic convergence to the least-norm variational equilibrium of the game is proven. Numerical examples show the effectiveness and efficiency of the proposed algorithms.