惩罚框架下求解广义Nash均衡问题的分解算法

广义Nash均衡问题(GNEP),是非合作博弈论中一类重要的问题,它在经济学、管理科学和交通规划等领域有着广泛的应用.本文主要提出一种新的惩罚算法来求解一般的广义Nash均衡问题,并根据罚函数的特殊结构,采用交替方向法求解子问题.在一定的条件下,本文证明新算法的全局收敛性.多个数值例子的试验结果表明算法是可行的,并且是有效的.

A decomposition method based on penalization for solving generalized Nash equilibrium problems

The generalized Nash equilibrium problem, GNEP for short, is a noncooperative game, which can be found wide applications in economics, management sciences and traffic assignment, etc. This paper presents a new penalty algorithm for solving the general GNEP, in which the alternating direction method is adopted to solve the subproblem according to the special structure of the penalty function. The global convergence of the new method is established under some assumptions. Preliminary numerical results demonstrate the proposed method is reliable and efficient.