On Coupling Constraints in Linear Bilevel Optimization
arxiv(2024)
摘要
It is well-known that coupling constraints in linear bilevel optimization can
lead to disconnected feasible sets, which is not possible without coupling
constraints. However, there is no difference between linear bilevel problems
with and without coupling constraints w.r.t. their complexity-theoretical
hardness. In this note, we prove that, although there is a clear difference
between these two classes of problems in terms of their feasible sets, the
classes are equivalent on the level of optimal solutions. To this end, given a
general linear bilevel problem with coupling constraints, we derive a
respective problem without coupling constraints and prove that it has the same
optimal solutions (when projected back to the original variable space).
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