二层随机规划逼近问题最优解集的上半收敛性

THE UPPER SEMI-CONVERGENCE OF OPTIMAL SOLUTION SETS OF APPROXIMATION PROBLEMS FOR BILEVEL STOCHASTIC PROGRAMMING

在下层初始随机规划问题可行解集上引入了正则的概念,并在下层初始随机规划最优解唯一的条件下,利用上图收敛理论,给出了下层随机规划逼近问题的任意一个最优解向量函数都连续收敛到下层初始随机规划问题的唯一最优解向量函数.然后将下层随机规划的最优解向量函数反馈到上层随机规划的目标函数和约束条件中,得到了上层随机规划逼近问题的最优解集关于最小信息概率度量收敛的上半收敛性.

In this paper, we define the concept of regularity of feasible set for lower level original stochastic programming. If optimal solution set for lower level original stochastic programming is a set of single points, by using the epi-convergence theory, we show that any optimal solution vector function for lower level stochastic programming approximation problem converges continuously to the unique optimal solution vector function for lower level original stochastic programming： Furthermore,if objective function and constraint conditions of upper level stochastic programming contain optimal solution vector function of lower level stochastic programming, if probability measure sequence is convergence, we obtain the upper semi-convergence of optimal solution set for upper level stochastic programming in minimal information probability metric.