随机规划逼近问题最优解集的下半收敛性

The Lower Semiconvergence of Optimal Solution Sets of Approximation Problems for Stochastic Programming

本文首先在无界且可积函数族对偶的概率测度空间上引入了最小信息概率度量,给出了这种概率度量收敛的充要条件及其与概率测度序列弱收敛的关系.然后在初始随机规划问题最优解集正则的条件下,利用最优解集的结构特征研究了随机规划逼近问题最优解集关于最小信息概率度量收敛的下半收敛性条件,从而得到了随机规划逼近最优解集Hausdorff收敛的一个充分条件.

This paper first introduces minimal information（m.i.） probability metric in duality spaces of unbounded integrable functions family, and gives the sufficient and necessary condition of the convergence in this probability metric and obtains the relationship between convergence in minimal information（m.i.） probability metric and weak convergence of probability measure sequence. Second, under the regularity condition of optimal solution sets for original stochastic programs, the lower semiconvergence condition of approximate optimal solution sets for stochastic programs is studied with structure characteristic, when the probability measure sequence is convergence in minimal information（m.i.） probability metric. Finally, a sufficient condition for Hausdorff convergence of approximate optimal solution sets in stochastic programs is obtained.