求解广义纳什均衡问题的指数型惩罚函数方法

本文利用指数型惩罚函数部分地惩罚耦合约束,从而将广义纳什均衡问题(GNEP)的求解转化为求解一系列光滑的惩罚纳什均衡问题 (NEP)。我们证明了若光滑的惩罚NEP序列的解序列的聚点处EMFCQ成立,则此聚点是 GNEP的一个解。进一步,我们把惩罚 NEP的KKT条件转化为一个非光滑方程系统,然后应用带有 Armijo 线搜索的半光滑牛顿法来求解此系统。最后,数值结果表明我们的指数型惩罚函数方法是有效的。

Exponential Penalty Function Method for Generalized Nash Equilibrium Problem

This paper reformulates the generalized Nash equilibrium problem(GNEP)as a sequence of smoothing penalized NEPs by means of a partial penalization of the coupling constraints where the exponential penalty functions are used. We demonstrate that the limit point is a solution to the GNEP under the EMFCQ at a limit point of solutions to smoothing penalized NEPs. Further more, we formulate the Karush-Kuhn-Tucker(KKT)conditions for smoothing penalized NEPs into a system of nonsmooth equations, and then apply the semismooth Newton method with Armijo line search to solve the system. Finally, the numerical results show that our exponential penalty function method for GNEP is effective.