线性二阶锥两阶段随机规划问题的统计推断
Statistical Inference of Two-Stage Linear Second-Order Conic Stochastic Programs
摘要: 在本篇文章中，我们考虑一类带有线性二阶锥约束的两阶段随机规划问题，该问题的全部参数都是随机变量。我们将原问题的最优值函数改写为一个包含紧致凸约束集合的极小极大问题，利用第二阶段问题的Lagrange对偶性质，得到其最优值函数的样本均值近似(SAA)估计的渐近分布。
Abstract: In this paper, we consider a linear second-order conic optimization problem and in which all pa-rameters are perturbed and random variables. We demonstrate that the optimal value function can be expressed as a min-max optimization problem over compact convex set, and we present the asymptotic distribution of an SAA estimator of the optimal value for a two-stage program whose second stage problem is a second-order conic programming problem.
文章引用：段庆松, 张立卫. 线性二阶锥两阶段随机规划问题的统计推断[J]. 应用数学进展, 2018, 7(7): 876-882. https://doi.org/10.12677/AAM.2018.77105

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