In this article, we present an inexact Newton method to solve generalized Nash equilibrium problems (GNEPs). Two types of GNEPs are studied: player convex and jointly convex. We reformulate the GNEP into an unconstrained optimization problem using a complementarity function and solve it by the proposed method. It is found that the proposed numerical scheme has the global convergence property for both types of GNEPs. The strong BD-regularity assumption for the reformulated system of GNEP plays a crucial role in global convergence. In fact, the strong BD-regularity assumption and a suitable choice of a forcing sequence expedite the inexact Newton method to Q-quadratic convergence. The efficiency of the proposed numerical scheme is shown for a collection of problems, including the realistic internet switching problem, where selfish users generate traffic. A comparison of the proposed method with the existing semi-smooth Newton method II for GNEP is provided, which indicates that the proposed scheme is more efficient.

在本文中，我们提出了一种不精确的牛顿方法来解决广义纳什均衡问题（GNEP）。研究了两种类型的 GNEP：玩家凸和联合凸。我们使用互补函数将 GNEP 重新表述为无约束优化问题，并通过所提出的方法对其进行求解。结果发现，所提出的数值格式对于两种类型的 GNEP 都具有全局收敛性。重新制定的 GNEP 体系的强 BD 正则性假设在全球收敛中发挥着至关重要的作用。事实上，强BD正则性假设和适当选择的强制序列加速了不精确牛顿法的Q二次收敛。所提出的数值方案的效率针对一系列问题得到了证明，包括现实的互联网切换问题，其中自私的用户产生流量。将所提出的方法与现有的 GNEP 半光滑牛顿法 II 进行比较，表明所提出的方案更加有效。