求解随机非线性互补问题的一种光滑化样本均值逼近方法

A Class of Smoothing SAA Methods for A Stochastic Nonlinear Complementarity Problem

提出一种基于光滑Fischer-Burmeister函数的光滑化样本均值逼近方法,并用该方法求解随机非线性互补问题,在适当的条件下,证明了光滑化SAA问题的最优解几乎处处指数收敛到真问题的最优解.算例的数值计算结果验证了算法的合理性和有效性.

A smoothing sample average approximation method based on a version of Fiseher-Burmeis- ter smoothing functions is proposed in this paper. It is used to solve the stochastic nonlinear complementar- ity problem. Under suitable conditions ,the almost sure convergence and exponential rate of this method is proved. The numerical test results indicate the efficiency of our method.