Adjustable robust optimization with objective uncertainty

Boris Detienne, Henri Lefebvre, Enrico Malaguti and Michele Monaci

European Journal of Operational Research, 2024, vol. 312, issue 1, 373-384

Abstract: In this work, we study optimization problems where some cost parameters are not known at decision time and the decision flow is modeled as a two-stage process within a robust optimization setting. We address general problems in which all constraints (including those linking the first and the second stages) are defined by convex functions and involve mixed-integer variables, thus extending the existing literature to a much wider class of problems. We show how these problems can be reformulated using Fenchel duality, allowing to derive an enumerative exact algorithm, for which we prove asymptotic convergence in the general case, and finite convergence for cases where the first-stage variables are all integer.

Keywords: Uncertainty modelling; Two-stage robust optimization; Reformulation; Fenchel duality; Branch-and-price; Computational experiments (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:312:y:2024:i:1:p:373-384

DOI: 10.1016/j.ejor.2023.06.042

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