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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 (respectively, allows limited) constraint violation for distributions residing (respectively, 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 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, ϕ-divergences, or moment conditions, as well as the event-wise ambiguity set. 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. History: Antonio Frangioni, Area Editor for Design & Analysis of Algorithms—Continuous. Funding: Z. Chen was supported by [General Research Fund Grant 9043424, NSFC/RGC Joint Research Scheme N_CityU105/21] from the Hong Kong Research Grants Council. S. Wang was supported by the National Natural Science Foundation of China [Grants 71922020, 72171221, and 71988101, entitled "Econometric Modeling and Economic Policy Studies"] and the Fundamental Research Funds for the Central Universities [Grant UCAS-E2ET0808X2]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0274) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2022.0274). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

We study adjustable distributionally robust optimization problems, where their ambiguity sets can potentially encompass an infinite number of expectation constraints. Although such ambiguity sets have 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 can be iteratively tightened to the infinitely constrained one. Through three numerical studies of adjustable distributionally robust optimization models, we show that our approach can yield improved solutions in a systematic way for both two-stage and multistage problems. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: Financial support by the Early Career Scheme from the Hong Kong Research Grants Council [Project No. CityU 21502820], the CityU Start-Up Grant [Project No. 9610481], the CityU Strategic Research Grant [Project No. 7005688], the National Natural Science Foundation of China [Project No. 72032005], and Chow Sang Sang Group Research Fund sponsored by Chow Sang Sang Holdings International Limited [Project No. 9229076] is gratefully acknowledged. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0181), as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0181). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]