广义纳什均衡问题求解的极小极大方法  

A minimax approach to solving generalized Nash equilibrium problem

作　　者：侯剑[1] 张立卫[1] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024

出　　处：《大连理工大学学报》2013年第6期924-929,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(11071029;91130007)

摘　　要：应用正则化Nikaido-Isoda函数,一类广义纳什均衡问题的求解被转化为一个极小极大问题的求解.利用Fischer-Burmeister函数将与极小极大问题的必要性条件等价的变分不等式的Karush-Kuhn-Tucker系统转化为一个半光滑方程组.应用牛顿法求解此方程组,并给出了半光滑牛顿法局部超线性收敛的充分条件.数值结果验证了极小极大方法对解决广义纳什均衡问题的有效性.Using the regularized Nikaido-Isoda function, the generalized Nash equilibrium problem is reformulated as a minimax problem. Based on Fischer-Burmeister function, the Karush-Kuhn-Tucker system of the variational inequality problem equivalent to the necessary conditions for this minimax problem, is transformed into a semismooth system of equations. The semismooth Newton method is used to solve the system and sufficient conditions for the local superlinear convergence of the semismooth Newton method are derived. Numerical results show that the minimax approach to solving the generalized Nash equilibrium problem is practical.

关 键 词：纳什均衡问题 广义纳什均衡问题 变分不等式 半光滑牛顿法 

分 类 号：O225[理学—运筹学与控制论]