We address mixed-integer linear bilevel programming. A discussion ofthe relationships between the optimistic and the pessimistic setting ispresented, providing necessary and sufficient conditions for them to beequivalent. A new class of inequalities, the follower optimality cuts, isintroduced and a related single-level non-compact reformulation of theproblem is derived. The same is done for a revision of a family of knowninequalities, the no-good cuts. A polyhedral comparison of the two for-mulations is carried out. Finally, we present a branch-and-cut algorithmbased on the follower optimality cuts and discuss computational results,comparing our algorithm with the best approaches in the literature, toshow its effectiveness.
working paper 30 dec 2020