随机规划经验逼近最优解集序列的几乎处处上半收敛性

The Almost Everywhere Upper Semiconvergence of the Optimal Solution Set Sequence of Empirical Approximations for Stochastic Programs

本文对随机规划经验逼近最优解集的几乎处处上半收敛性进行了研究。首先通过经验概率测度替代初始规划的概率测度得到随机规划的经验逼近模型,然后将带有约束的随机规划问题转化成与其等价的无约束的随机规划问题,最后利用上图收敛性理论,给出了随机规划经验逼近最优解集的几乎处处上半收敛性。本文采用的经验逼近方法可应用于研究随机规划统计估计问题的一致相合性、稳健性、极大似然估计的强相合性。

This paper discussed almost everywhere upper semiconvergence of optimal solution set of empirical approximations for stochastic programs. Firstly, an empirical approximation model of stochastic programming is obtained by replacing the probability measure of original program with empirical probability measure. Sequentially, the constrained stochastic programming is transformed into an equivalent unconstrained stochastic programming. Finally, using the epi-convergence theory, the almost everywhere upper semiconvergence of optimal solution set of empirical approximations for stochastic programming is obtained. The empirical approximation methods can be applied to study uniform consistency, robustness, strong consistency of the maximum likelihood estimator of statistical estimators.