CAJ | 학술논문

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。
응용정칙화Nikaido-Isoda함수，일류엄의납십균형문제적구해피전화위일개겁소겁대문제적구해。이용Fischer-Burmeister함수장여겁소겁대문제적필요성조건등개적변분불등식적Karush-Kuhn-Tucker계통전화위일개반광활방정조。응용우돈법구해차방정조，병급출료반광활우돈법국부초선성수렴적충분조건。수치결과험증료겁소겁대방법대해결엄의납십균형문제적유효성。
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 New ton method are derived . Numerical results show that the minimax approach to solving the generalized Nash equilibrium problem is practical .