Distributionally robust chance constraints for non-linear uncertainties
Distributionally robust chance constraints for non-linear uncertainties
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DOI：
10.1007/s10107-014-0842-5
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发表时间：
2014-11
影响因子：
2.7
通讯作者：
Wenzhuo Yang;Huan Xu
中科院分区：
文献类型：
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作者：
Wenzhuo Yang;Huan Xu
本文研究分布鲁棒机会约束优化问题的计算问题。与以前主要关注线性情况的研究不同(除了下面详细讨论的一些例外情况)，我们考虑了约束对决策变量，特别是对不确定参数可能是非线性的情况。这一公式非常有意义，因为它可以模拟应用中普遍存在的非线性不确定性。我们的主要结果表明，如果不确定性由其均值和方差来表征，且约束函数在决策变量中是凹的，在不确定参数中是拟凸的，则分布鲁棒机会约束优化是可处理的。在此过程中，我们建立了分布稳健机会约束和以确定性方式模拟不确定性的稳健优化框架之间的等价关系。这将在不确定情况下的决策中的两个广泛应用的范例联系在一起，并将以前在线性情况下相同精神的结果扩展到更一般的情况。然后，我们考虑概率包络约束，这是徐等人首先提出的分布稳健机会约束的推广。(Oper Res 60：682-700,2012)。我们将该框架推广到非线性情形，并推导出保证其可处理性的充分条件。最后，我们研究了联合概率包络约束的可处理逼近，并给出了这些近似公式可处理的条件。
This paper investigates the computational aspects of distributionally robust chance constrained optimization problems. In contrast to previous research that mainly focused on the linear case (with a few exceptions discussed in detail below), we consider the case where the constraints can be non-linear to the decision variable, and in particular to the uncertain parameters. This formulation is of great interest as it can model non-linear uncertainties that are ubiquitous in applications. Our main result shows that distributionally robust chance constrained optimization is tractable, provided that the uncertainty is characterized by its mean and variance, and the constraint function is concave in the decision variables, and quasi-convex in the uncertain parameters. En route, we establish an equivalence relationship between distributionally robust chance constraint and the robust optimization framework that models uncertainty in a deterministic manner. This links two broadly applied paradigms in decision making under uncertainty and extends previous results of the same spirit in the linear case to more general cases. We then consider probabilistic envelope constraints, a generalization of distributionally robust chance constraints first proposed in Xu et al. (Oper Res 60:682–700, 2012) for the linear case. We extend this framework to the non-linear case, and derive sufficient conditions that guarantee its tractability. Finally, we investigate tractable approximations of joint probabilistic envelope constraints, and provide the conditions when these approximation formulations are tractable.