Paper ID: 2408.13323

Stable Formulations in Optimistic Bilevel Optimization

Johannes O. Royset

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.

Submitted: Aug 23, 2024