We extend the notion of globalized robustness to consider distributional information beyond the support of the ambiguous probability distribution. We propose the globalized distributionally robust counterpart that disallows any (resp., allows limited) constraint violation for distributions residing (resp., not residing) in the ambiguity set. By varying its inputs, our proposal recovers several existing perceptions of parameter uncertainty. Focusing on the type-$1$ Wasserstein distance, we show that the globalized distributionally robust counterpart has an insightful interpretation in terms of \textit{shadow price of globalized robustness}, and it can be seamlessly integrated with many popular optimization models under uncertainty without incurring any extra computational cost. Such computational attractiveness also holds for other ambiguity sets, including the ones based on probability metric, optimal transport, $\phi$-divergences, or moment conditions. Numerical studies on an adaptive network lot-sizing problem demonstrate the modeling flexibility of our proposal and its emphases on globalized robustness to constraint violation.
Citation
University of Chinese Academy of Sciences, working paper.