Dependence of bilevel mathematical programs on irrelevant constraints

For standard, single-level mathematical programs, any optimal solution remains optimal when an inactive (i.e., irrelevant) constraint is added to the problem, a property termed independence of irrelevant constraints (IIC). In general, bilevel mathematical programs do not possess the IIC property. This paper presents necessary and sufficient conditions for the IIC property to hold for a bilevel program. A straightforward test is described that concludes whether or not a bilevel program is IIC.