We propose a single-level reformulation (SLR) for pessimistic bilevel optimization that does not rely on complementarity conditions or optimal value functions. For this reason, we refer to it as a true single-level reformulation (tSLR). A remarkable consequence is that this formulation can satisfy the classical linear independence constraint qualification, despite the fact that even the weaker Mangasarian–Fromovitz constraint qualification is known to systematically fail for standard single-level reformulations of both optimistic and pessimistic bilevel programs. Furthermore, the necessary optimality conditions induced by the tSLR can be expressed as a square system of equations, making them directly computable by any semismooth Newton solver. Leveraging this reformulation, we also derive the first sufficient conditions guaranteeing that a Karush–Kuhn–Tucker point of a pessimistic bilevel program is a local optimum. Numerical experiments demonstrate that algorithms based on the proposed tSLR can significantly outperform existing approaches for pessimistic bilevel optimization. Overall, the proposed framework suggests that pessimistic bilevel programs may be considerably more tractable than previously believed and need not be inherently more difficult to solve than their optimistic counterparts.
Citation
Oliver Stein and Alain Zemkoho (2026). A true single–level reformulation for pessimistic bilevel optimization, https://optimization-online.org/?p=35995