Stability Analysis for Mathematical Programs with Distributionally Robust Chance Constraint ∗
Stability Analysis for Mathematical Programs with Distributionally Robust Chance Constraint ∗
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发表时间：
2015
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通讯作者：
Shaoyan Guo;Huifu Xu;Liwei Zhang
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作者：
Shaoyan Guo;Huifu Xu;Liwei Zhang
机会约束优化问题的稳定性分析主要关注机会约束中概率测度的变化对最优值和最优解的影响，在随机规划的文献中已有大量的研究。在本文中，我们扩展这样的分析与分布强大的机会约束的优化问题，其中真正的概率是未知的，但它是可能的，以构建一个模糊的分布集和机会约束是基于最保守的选择的概率分布的模糊集。稳定性分析着重于模糊度集的变化对最优值和最优解的影响。我们首先研究了鲁棒概率函数的连续性，然后详细分析了函数的近似。给出了最优值连续和最优解集外连续的充分条件。实例研究进行了模糊集正在通过时刻和样本构建。
Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability is unknown, but it is possible to construct an ambiguity set of distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set. The stability analysis focuses on impact of the variation of the ambiguity set on the optimal value and optimal solutions. We start by looking into continuity of the robust probability function and followed with a detailed analysis of approximation of the function. Sufficient conditions have been derived for continuity of the optimal value and outer semicontinuity of optimal solution set. Case studies are carried out for ambiguity sets being constructed through moments and samples.