Distributed Generalized Nash Equilibrium Seeking for Monotone Generalized Noncooperative Games by a Regularized Penalized Dynamical System
针对带有集合约束和共享仿射不等式约束的单调广义非合作博弈，提出一种基于投影梯度的正则化惩罚动力系统，并设计分布式算法，证明其渐近收敛到最小范数变分均衡。
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.