数据驱动的分布式鲁棒随机二次规划的收敛性分析

Convergence Analysis of Data-Driven Distributionally Robust Stochastic Quadratic Programming

摘要: 本文研究数据驱动的Wasserstein模糊集下分布式鲁棒随机二次规划的收敛性问题。首先，我们建立了目标函数的逐点Lipschitz性质。接着，当样本量趋于无穷大时，利用大数定律，Helly-Bray定理给出了分布式目标函数收敛于目标函数的期望值。最后，我们建立了分布式鲁棒随机二次规划收敛于通常的随机二次规划问题。

Abstract: In this paper, we study the convergence problem of distributionally robust stochastic quadratic programming under the data-driven Wasserstein ambiguity sets. First, we establish the point-by-point Lipschitz property of the objective function. Then, when the sample size tends to infinity, using the law of large numbers, the Helly-Bray theorem derives the expectation of the distributionally objective function converges to the objective function. Finally, we establish that the distributionally robust stochastic quadratic programming converges to the general stochastic quadratic programming problem.