This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from the renowned Arrow-Debreu general economic equilibrium model. While the latter model is the foundation of much of mathematical economics, the GNEP provides a mathematical model of multi-agent non-cooperative competition that has found many contemporary applications in diverse engineering domains. The most salient feature of the GNEP that distinguishes it from a standard non-cooperative (Nash) game is that each player's optimization problem contains constraints that couple all players' decision variables. Extending results for stand-alone optimization problems, the penalization theory aims to convert the GNEP into a game of the standard kind without the coupled constraints, which is known to be more readily amenable to solution methods and analysis. Starting with an illustrative example to motivate the development, the paper focuses on two kinds of coupled constraints, shared (i.e., common) and finitely representable. Constraint residual functions and the associated error bound theory play an important role throughout the development.

中文翻译：

---

广义Nash平衡问题的精确罚分

本文提出了广义纳什均衡问题（GNEP）的精确惩罚理论，该理论起源于著名的Arrow-Debreu一般经济均衡模型。尽管后者模型是许多数学经济学的基础，但GNEP提供了一种多主体非合作竞争的数学模型，该模型已经在多种工程领域中找到了许多当代应用。GNEP与标准非合作（Nash）游戏的区别最突出的特点是，每个玩家的优化问题都包含将所有玩家的决策变量耦合在一起的约束。惩罚理论扩展了独立优化问题的结果，旨在将GNEP转换为标准类型的博弈，而无需耦合约束，众所周知，它更容易适用于求解方法和分析。从一个激励发展的说明性示例开始，本文着重于两种耦合约束，即共享（即公共）约束和可有限表示的约束。约束残差函数和相关的误差界限理论在整个开发过程中都起着重要作用。