Van Zyl, Gusti2025-09-022025-09-022025Gusti van Zyl (29 May 2024): A minimax approach to duality for linear distributional sensitivity testing, Optimization, DOI: 10.1080/02331934.2024.2358410.0233-1934 (print)1029-4945 (online)10.1080/02331934.2024.2358410http://hdl.handle.net/2263/104167We consider the dual formulation of the problem of finding the maximum of 𝔼𝜈⁡[𝑓⁡(𝑋)], where ν is allowed to vary over all the probability measures on a Polish space 𝒳 for which 𝑑𝑐⁡(𝜇,𝜈)≤𝑟, with 𝑑𝑐 an optimal transport distance, f a real-valued function on 𝒳 satisfying some regularity, μ a ‘baseline’ measure and 𝑟≥ 0. Whereas some derivations of the dual rely on Fenchel duality, applied on a vector space of functions in duality with a vector space of measures, we impose compactness on 𝒳 to allow the use of the minimax theorem of Ky Fan, which does not require vector space structure.en© 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/).DualityMinimaxSensitivity testingDistributionally robust computationArticle