We study adjustable distributionally robust optimization problems where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such an ambiguity set has great modeling flexibility in characterizing uncertain probability distributions, the corresponding adjustable problems remain computationally intractable and challenging. To overcome this issue, we propose a greedy improvement procedure that consists of solving, via the (extended) linear decision rule approximation, a sequence of tractable subproblems---each of which considers a relaxed and finitely constrained ambiguity set that is also iteratively tightened to the infinitely constrained one. Through three numerical studies of adjustable distributionally robust optimization models that consider complete covariance information, we show that our approach can yield improved solutions in a systematic way for both two-stage and multi-stage operations management problems.
City University of Hong Kong, working paper