On Coupling Constraints in Pessimistic Linear Bilevel Optimization

Jointly with Dorothee Henke, Martin Schmidt and Johannes Thürauf

Year: 2025

Abstract: The literature on pessimistic 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.

Cite as:

@techreport{henke2025coupling,
  title={On Coupling Constraints in Pessimistic Linear Bilevel Optimization},
  author={Dorothee Henke and Henri Lefebvre and Martin Schmidt and Johannes Thürauf},
  year={2025},
  archivePrefix={Optimization Online},
  url={https://optimization-online.org/?p=29476}
}

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Optimization Online - arXiv

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