The decision problem for the optimal objective value (and unboundedness) of a k-level linear program is Σ^p_{k-1}-complete.
BilevellinearoptimizationbelongstoNPandadmitspolynomial- size KKT-based reformulations
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Pessimistic linear bilevel optimization problems with coupling constraints are equivalent to pessimistic and optimistic versions without them.
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Decision Problems in Multilevel Linear Programming
The decision problem for the optimal objective value (and unboundedness) of a k-level linear program is Σ^p_{k-1}-complete.
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On Coupling Constraints in Pessimistic Linear Bilevel Optimization
Pessimistic linear bilevel optimization problems with coupling constraints are equivalent to pessimistic and optimistic versions without them.