Stable Formulations in Optimistic Bilevel Optimization
<|reference_start|>Stable Formulations in Optimistic Bilevel Optimization: Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted, alternative formulation that exhibits desirable stability properties under mild assumptions that neither invoke convexity nor smoothness. The upper- and lower-level problems might involve integer restrictions and disjunctive constraints. In a range of results, we at most invoke pointwise and local calmness for the lower-level problem in a sense that holds broadly. The alternative formulation is computationally attractive with structural properties being brought out and an outer approximation algorithm becoming available.<|reference_end|>
@article{royset2024stable,
    title={Stable Formulations in Optimistic Bilevel Optimization},
    author={Johannes O. Royset},
    journal={arXiv preprint arXiv:2408.13323},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.13323},
    primaryClass={math.OC cs.LG cs.SY eess.SY}
}