求解随机二阶锥互补问题的期望值模型及其近似问题的收敛性分析

Expected value model for solving stochastic second-order-cone complementarity problem and convergence analysis of its approximation problems

利用二阶锥互补函数φ_(NR)给出求解随机二阶锥互补问题的确定期望值(EV)模型.由于该模型的目标函数非光滑,利用光滑化方法给出该模型的光滑化近似问题.当期望值可以求得时,考虑了光滑近似问题的收敛性结果.当期望值不易求得时,利用样本均值近似方法给出光滑化样本均值近似问题,并考虑了当光滑参数不变的情况下,光滑化样本均值近似问题的收敛性结果.

The deterministic expected value(EV)model for solving stochastic second-order cone complementarity problem is given by using the second-order cone complementary function^n r-Since the objective function of the model is not smooth,the smoothing method is used to give the model's smoothing approximation problem.When the expected value can be calculated,the convergence results of the smoothing approximation problem are taken into account.When the expected value is not easy to be calculated,the smoothing sample average approximation problem is given by using the sample average approximation method.And the convergence result of the smoothing sample average approximation problem is considered,when the smoothing parameter is fixed.