Connections and Reformulations between Robust and Bilevel Optimization

Submission Status:under review
  • Robust and bilevel optimization share the common feature that they involve a certain multilevel structure. Hence, although they model something rather different when used in practice, they seem to have a similar mathematical structure. In this paper, we analyze the connections between different types of robust problems (strictly robust problems with and without decision-dependence of their uncertainty sets, min-max-regret problems, and two-stage robust problems) as well as of bilevel problems (optimistic problems, pessimistic problems, and robust bilevel problems). It turns out that bilevel optimization seems to be more general in the sense that for most types of robust problems, one can find proper reformulations as bilevel problems but not necessarily the other way around. We hope that these results pave the way for a stronger connection between the two fields - in particular to use both theory and algorithms from one field in the other and vice versa.

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Author:Marc Goerigk, Jannis Kurtz, Martin Schmidt, Johannes Thürauf
Document Type:Preprint
Date of Publication (online):2023/06/27
Release Date:2023/06/27
Tag:Bilevel optimization; Reformulations; Robust optimization
Page Number:20
Institutes:Universität Trier
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International