Aug 2024· SIAM Journal on Optimization· Vol 36, pp. 987-1016· 2 citations· 50 references
MathematicsComputer ScienceEngineering
TL;DR
This work constructs a lifted formulation that exhibits desirable stability properties under mild assumptions that neither invoke convexity nor smoothness for the lower-level problem in a sense that holds broadly.
Abstract
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.
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