Exact Penalization of Generalized Nash Equilibrium Problems

• 成果类型: Article; Early Access
• 署名作者: Ba, Qin; Pang, Jong-Shi
• 署名单位: University of Southern California
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2019.1942
• 发表日期: 2020
• 关键词: generalized Nash games; exact penalization; error bounds; constraint qualifications

摘要

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. Whereas the latter model is the foundation of much of mathematical economics, the GNEP provides a mathematical model of multiagent noncooperative competition that has found many contemporary applications in diverse engineering domains. The most salient feature of the GNEP that distinguishes it from a standard noncooperative (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, this 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.