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This paper presents a new primal-dual method for computing an equilibrium of generalized (continuous) Nash game (referred to as generalized Nash equilibrium problem (GNEP)) where each player's feasible strategy set depends on the other…

Computer Science and Game Theory · Computer Science 2022-03-04 Jong Gwang Kim

This paper studies convex Generalized Nash Equilibrium Problems (GNEPs) that are given by polynomials. We use rational and parametric expressions for Lagrange multipliers to formulate efficient polynomial optimization for computing…

Optimization and Control · Mathematics 2021-11-09 Jiawang Nie , Xindong Tang

This paper studies generalized Nash equilibrium problems that are given by rational functions. The optimization problems are not assumed to be convex. Rational expressions for Lagrange multipliers and feasible extensions of KKT points are…

Optimization and Control · Mathematics 2023-02-23 Jiawang Nie , Xindong Tang , Suhan Zhong

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…

Optimization and Control · Mathematics 2018-07-13 Christian Kanzow , Daniel Steck , Daniel Wachsmuth

We consider the problem of computing an equilibrium in a class of \textit{nonlinear generalized Nash equilibrium problems (NGNEPs)} in which the strategy sets for each player are defined by equality and inequality constraints that may…

Optimization and Control · Mathematics 2023-02-07 Michael I. Jordan , Tianyi Lin , Manolis Zampetakis

We study generalized Nash equilibrium problems (GNEPs) such that objectives are polynomial functions, and each player's constraints are linear in their own strategy. For such GNEPs, the KKT sets can be represented as unions of simpler sets…

Optimization and Control · Mathematics 2024-05-30 Jiyoung Choi , Jiawang Nie , Xindong Tang , Suhan Zhong

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used,…

Robotics · Computer Science 2025-11-07 Mark Pustilnik , Francesco Borrelli

Generalized Nash equilibrium problems (GNEPs) arise in various applications where multiple players minimize individual cost functions subject to coupled constraints. A relatively unexplored approach to solving such problems is via a…

Optimization and Control · Mathematics 2026-05-12 Ruoyu Diao , Yu-Hong Dai , Liwei Zhang

Generalized Nash Equilibrium Problems (GNEPs) arise in many applications, including non-cooperative multi-agent control problems. Although many methods exist for finding generalized Nash equilibria, most of them rely on assuming knowledge…

Computer Science and Game Theory · Computer Science 2026-03-19 Pablo Krupa , Alberto Bemporad

The equilibrium selection problem in the variational Generalized Nash Equilibrium Problem (v-GNEP) has been reported as an optimization problem defined over the solution set of v-GNEP, called in this paper the lower-level v-GNEP. However,…

Optimization and Control · Mathematics 2025-08-19 Shota Matsuo , Keita Kume , Isao Yamada

We consider generalized Nash equilibrium problems (GNEPs) with linear coupling constraints affected by both local (i.e., agent-wise) and global (i.e., shared resources) disturbances taking values in polyhedral uncertainty sets. By making…

Systems and Control · Electrical Eng. & Systems 2023-04-07 Marta Fochesato , Filippo Fabiani , John Lygeros

This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…

Optimization and Control · Mathematics 2022-04-20 Xiaoxi Jia , Christian Kanzow , Patrick Mehlitz , Gerd Wachsmuth

We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few…

Computer Science and Game Theory · Computer Science 2024-04-10 Tobias Harks , Julian Schwarz

For generalized Nash equilibrium problems (GNEP) with shared constraints we focus on the notion of normalized Nash equilibrium in the nonconvex setting. The property of nondegeneracy for normalized Nash equilibria is introduced.…

Optimization and Control · Mathematics 2022-05-30 Vladimir Shikhman

This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss-Seidel method and Lasserre type Moment-SOS relaxations to solve GNEPPs. The convergence of the Gauss-Seidel method is known for some…

Optimization and Control · Mathematics 2020-09-08 Jiawang Nie , Xindong Tang , Lingling Xu

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Numerical Analysis · Mathematics 2025-06-16 Jianchao Bai , Linyuan Jia , Zheng Peng

In dynamic games with shared constraints, Generalized Nash Equilibria (GNE) are often computed using the normalized solution concept, which assumes identical Lagrange multipliers for shared constraints across all players. While widely used,…

Robotics · Computer Science 2025-04-10 Mark Pustilnik , Antonio Loquercio , Francesco Borrelli

In this paper, we consider stochastic monotone Nash games where each player's strategy set is characterized by possibly a large number of explicit convex constraint inequalities. Notably, the functional constraints of each player may depend…

Optimization and Control · Mathematics 2023-08-25 Zeinab Alizadeh , Afrooz Jalilzadeh , Farzad Yousefian

In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…

Computer Science and Game Theory · Computer Science 2017-03-27 Farzad Salehisadaghiani , Lacra Pavel

We propose a learning-based approach for approximating solution mappings of multiparametric generalized Nash equilibrium problems (GNEPs) with coupling in both objectives and constraints. Rather than solving a standard regression problem on…

Optimization and Control · Mathematics 2026-05-28 A. Bemporad , T. Tatarenko
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