二层随机规划逼近解集上半收敛性的一个充分条件

On a Sufficient Condition of Upper Semi-Convergence of Approximation Solution Set for Bi-Level Stochastic Programming

针对上、下层都含有目标函数和约束条件的一类二层随机规划逼近问题,首先在下层随机规划的目标函数和约束条件均为严格凸函数的情况下,给出了下层随机规划逼近问题的任意一个最优解序列连续收敛于下层随机规划的唯一最优解的一个充分条件;然后将下层随机规划的最优解反馈到上层随机规划的目标函数和约束条件,得到了上层随机规划逼近最优解集的上半收敛性.

For a class of bi-level stochastic programming approximation problem in which the upper and lower level contain objective function and constrains.In this paper,under the conditions that the objective function and constraint conditions of the lower level stochastic programming are all strictly convex function,we have given the sufficient condition that a arbitrary optimal solution sequence of the lower level programming approximation problem continuous converges the only optimal solution.The optimal solution of lower stochastic programming provide feedback to the objective function and constraint conditions of the upper,then we obtain the upper semi-convergence of the approximate optimal solution set for the upper.