On Coupling Constraints in Pessimistic Linear Bilevel Optimization
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914535873445888 |
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| author | Henke, Dorothee Lefebvre, Henri Schmidt, Martin Thürauf, Johannes |
| author_facet | Henke, Dorothee Lefebvre, Henri Schmidt, Martin Thürauf, Johannes |
| contents | The literature on pessimistic linear bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this note, we show that this is not the case. To this end, given a pessimistic problem with coupling constraints, we derive a pessimistic problem without coupling constraints that has the same set of globally optimal solutions. Moreover, our results also show that one can equivalently replace a pessimistic problem with such constraints with an optimistic problem without coupling constraints. This paves the way of both transferring theory and solution techniques from any type of these problems to any other one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Coupling Constraints in Pessimistic Linear Bilevel Optimization Henke, Dorothee Lefebvre, Henri Schmidt, Martin Thürauf, Johannes Optimization and Control 91A65 The literature on pessimistic linear bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this note, we show that this is not the case. To this end, given a pessimistic problem with coupling constraints, we derive a pessimistic problem without coupling constraints that has the same set of globally optimal solutions. Moreover, our results also show that one can equivalently replace a pessimistic problem with such constraints with an optimistic problem without coupling constraints. This paves the way of both transferring theory and solution techniques from any type of these problems to any other one. |
| title | On Coupling Constraints in Pessimistic Linear Bilevel Optimization |
| topic | Optimization and Control 91A65 |
| url | https://arxiv.org/abs/2503.01563 |