Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls
证明两阶段鲁棒和分布鲁棒线性规划可精确重构为锥规划，当模糊集为离散分布中心的Wasserstein球时，问题等价于协正规划或可被序列逼近，并基于半定规划给出可处理近似。
Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions. Specifically, when the ambiguity set constitutes a 2-Wasserstein ball centered at a discrete distribution, the distributionally robust linear program is equivalent to a copositive program (if the problem has complete recourse) or can be approximated arbitrarily closely by a sequence of copositive programs (if the problem has sufficiently expensive recourse). These results directly extend to the classical robust setting and motivate strong tractable approximations of two-stage problems based on semidefinite approximations of the copositive cone. We also demonstrate that the two-stage distributionally robust optimization problem is equivalent to a tractable linear program when the ambiguity set constitutes a 1-Wasserstein ball centered at a discrete distribution and there are no support constraints. The online appendix is available at https://doi.org/10.1287/opre.2017.1698 .