A unified theory of robust and distributionally robust optimization via the primal-worst-equals-dual-best principle
File(s)
Accepted version
Author(s)
Zhen, Jianzhe
Kuhn, Daniel
Wiesemann, Wolfram
Type
Journal Article
Abstract
Robust optimization and distributionally robust optimization are modeling paradigms for decision making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the uncertainty. In this paper, we develop a rigorous and general theory of robust and distributionally robust nonlinear optimization using the language of convex analysis. Our framework is based on a generalized “primal-worst-equals-dual-best” principle that establishes strong duality between a semi-infinite primal worst and a nonconvex dual best formulation, both of which admit finite convex reformulations. This principle offers an alternative formulation for robust optimization problems that obviates the need to mobilize the machinery of abstract semi-infinite duality theory to prove strong duality in distributionally robust optimization. We illustrate the modeling power of our approach through convex reformulations for distributionally robust optimization problems whose ambiguity sets are defined through general optimal transport distances, which generalize earlier results for Wasserstein ambiguity sets.
Date Issued
2025-03-01
Date Acceptance
2023-07-06
Citation
Operations Research, 2025, 73 (2), pp.862-878
ISSN
0030-364X
Publisher
Institute for Operations Research and Management Sciences
Start Page
862
End Page
878
Journal / Book Title
Operations Research
Volume
73
Issue
2
Copyright Statement
Copyright © 2023, INFORMS
For the purpose of open access, the authors have applied a ‘Creative Commons Attribution (CC
BY) licence to any Author Accepted Manuscript (AAM) version arising
For the purpose of open access, the authors have applied a ‘Creative Commons Attribution (CC
BY) licence to any Author Accepted Manuscript (AAM) version arising
License URL
Identifier
https://pubsonline.informs.org/doi/full/10.1287/opre.2021.0268
Publication Status
Published
Date Publish Online
2023-09-26