2025/12/09 by Harwood, Stuart M., Papageorgiou, Dimitri J.
Computer Science · Decision Sciences · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · doi:10.48550/arxiv.2512.08770
openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28
Generalized Nash equilibrium (GNE) is a solution concept for complete information games, in which each player's objective function and feasible region depend on other players' actions. While numerical methods for finding GNE when players possess convex structure are relatively mature, the same cannot be said when players optimize nonconvex objective functions over nonconvex feasible regions. Drawing inspiration from the notion of a normalized (or variational) Nash equilibrium, which is a more restrictive class of solutions to generalized Nash games, we extend the ideas of Harwood et al. ("Equilibrium modeling and solution approaches inspired by nonconvex bilevel programming." Computational Optimization and Applications, 87(2):641-676, 2024) to develop an exact method that can find a normalized Nash equilibrium (NNE) of a problem, when such an NNE exists. By adapting the framework of Harwood et al., we are able to find NNE without any convexity assumptions. We demonstrate the effectiveness of our method on several nonconvex games.