TY - EJOUR
DO - 10.1287/opre.2017.1698
AB - 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, then 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.
T1 - Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls
IS - 3
DA - 2018
AU - Hanasusanto, Grani
AU - Kuhn, Daniel
JF - Operations Research
SP - 849-869
VL - 66
EP - 849-869
N1 - Available from Optimization Online
ID - 221453
KW - Two-stage problems
KW - Robust optimization
KW - Distributionally robust optimization
KW - Copositive programming
UR - http://www.optimization-online.org/DB_HTML/2016/09/5647.html
ER -