Connections between Robust and Bilevel Optimization
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 type...
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| Format: | Article |
| Language: | English |
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Université de Montpellier
2025-01-01
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| Series: | Open Journal of Mathematical Optimization |
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| Online Access: | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.38/ |
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| author | Goerigk, Marc Kurtz, Jannis Schmidt, Martin Thürauf, Johannes |
| author_facet | Goerigk, Marc Kurtz, Jannis Schmidt, Martin Thürauf, Johannes |
| author_sort | Goerigk, Marc |
| collection | DOAJ |
| description | 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 (static robust problems with and without decision-dependence of their uncertainty sets, worst-case 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. |
| format | Article |
| id | doaj-art-1f0b185a778646209f64768f0a6cc167 |
| institution | Kabale University |
| issn | 2777-5860 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Université de Montpellier |
| record_format | Article |
| series | Open Journal of Mathematical Optimization |
| spelling | doaj-art-1f0b185a778646209f64768f0a6cc1672025-02-07T14:03:16ZengUniversité de MontpellierOpen Journal of Mathematical Optimization2777-58602025-01-01611710.5802/ojmo.3810.5802/ojmo.38Connections between Robust and Bilevel OptimizationGoerigk, Marc0Kurtz, Jannis1Schmidt, Martin2Thürauf, Johannes3University of Passau, Business Decisions and Data Science, Dr.-Hans-Kapfinger Str. 30, 94032 Passau, GermanyAmsterdam Business School, University of Amsterdam, 1018 TV Amsterdam, NetherlandsTrier University, Department of Mathematics, Universitätsring 15, 54296 Trier, GermanyUniversity of Technology Nuremberg (UTN), Department Liberal Arts and Social Sciences, Discrete Optimization Lab, Dr.-Luise-Herzberg-Str. 4, 90461 Nuremberg, GermanyRobust 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 (static robust problems with and without decision-dependence of their uncertainty sets, worst-case 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.https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.38/Bilevel optimizationRobust optimizationReformulations |
| spellingShingle | Goerigk, Marc Kurtz, Jannis Schmidt, Martin Thürauf, Johannes Connections between Robust and Bilevel Optimization Open Journal of Mathematical Optimization Bilevel optimization Robust optimization Reformulations |
| title | Connections between Robust and Bilevel Optimization |
| title_full | Connections between Robust and Bilevel Optimization |
| title_fullStr | Connections between Robust and Bilevel Optimization |
| title_full_unstemmed | Connections between Robust and Bilevel Optimization |
| title_short | Connections between Robust and Bilevel Optimization |
| title_sort | connections between robust and bilevel optimization |
| topic | Bilevel optimization Robust optimization Reformulations |
| url | https://ojmo.centre-mersenne.org/articles/10.5802/ojmo.38/ |
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