On Stability in Optimistic Bilevel Optimization
This addresses stability issues in bilevel optimization for applications involving integer and disjunctive constraints, though it appears incremental as it builds on existing formulations.
The paper tackles the instability of solutions in optimistic bilevel optimization problems under data changes by constructing a lifted formulation that exhibits stability without requiring convexity or smoothness, and demonstrates computational attractiveness with an outer approximation algorithm.
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted 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 invoke at most pointwise and local calmness for the lower-level problem in a sense that holds broadly. The lifted formulation is computationally attractive with structural properties being brought out and an outer approximation algorithm becoming available.