Inexact Newton Method for Solving Generalized Nash Equilibrium Problems

Abstract

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. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.