二层随机规划逼近最优解集的上半收敛性

The upper semi-convergence of the optimal solution set of approximation for bi-level stochastic programming

下层随机规划以上层决策变量作为参数,而上层随机规划是以下层随机规划的唯一最优解作为响应的一类二层随机规划问题,首先在下层随机规划的原问题有唯一最优解的假设下,讨论了下层随机规划的任意一个逼近最优解序列都收敛于原问题的唯一最优解,然后将下层随机规划的唯一最优解反馈到上层,得到了上层随机规划逼近最优解集序列的上半收敛性.

A bi-level stochastic programming problem where the upper level stochastic programming is an op-timization problem including a parametric unique optimal solution of the lower level stochastic programming, and the lower level stochastic programming is a parametric nonlinear programming including the decision vari-ables of the upper level stochastic programming as parameters. This paper first discusses the assumption that the lower level stochastic programming has unique optimal solution of the original problem, any approximation optimal solution sequence of the lower level stochastic programming converges to the unique optimal solution of the original problem. And then feedbacks the unique optimal solution of lower level stochastic programming to the upper level, obtains the upper semi-convergence of the upper level stochastic programming approximation optimal solution sequence.