摘要
主要考虑随机广义纳什均衡问题(SGNEP),由于随机变量的存在,SGNEP通常无解.对此问题,文章首先给出一阶必要性条件并利用NCP函数得到优化模型的目标函数,为降低所得解的"风险",再利用条件风险价值(CVaR)给出约束条件,从而构造出求解SGNEP的一个低风险模型,并将此模型所得解视为SGNEP的解.然而,直接求解该低风险模型可能会遇到两个问题:一是该模型含有非光滑约束,二是目标函数和约束条件包含期望值.考虑到这两个问题,采用光滑化和罚样本均值近似方法提出该模型的近似问题,并进一步给出近似问题最优解的收敛性结果.最后,文章给出数值算例,以验证所提方法的可行性.
In this paper, we consider stochastic generalized Nash equilibrium prob- lems （SGNEP）. As a result of the existence of random variable, the SGNEP may have no solutions. In order to deal with this problem, we first give the first order necessary condition and employ NCP function to obtain the objective function of optimization model. To reduce the ＂risk＂ of the solutions, we again use conditional value-at-risk （CVaR） to give constraints. Thus, we construct a low risk model of the SGNEP. The solutions of the model can be regarded as those of SGNEP. However, there may be two difficulties for solving the low risk model directly： One is that the constraints are non-smooth, the other is that the objective and constraints contain expectations. In view of these two problems, we present approximation problems of the model by using smoothing method and penalized sample average approximation （SAA） technique. Furthermore, we give convergence results of optimal solutions of the approximation problems. Numerical examples are presented to verify the feasibility of the proposed methods.
出处
《系统科学与数学》
CSCD
北大核心
2016年第12期2408-2420,共13页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11501275)
辽宁省教育厅科学研究一般项目(L2015199)资助课题
关键词
NCP函数
条件风险价值
期望残差最小化
光滑化
罚样本均值近似
NCP function, conditional value-at-risk, expected residual minimization, smoothing, penalized sample average approximation.
