Dependence of bilevel mathematical programs on irrelevant constraints

摘要

A bilevel program (BP) is a mathematical program with two levels. The objective function and constraint space of the second-level problem are parameterized on the variables of the-first-level problem. For standard, single-level mathematical programs, any optimal solution remains optimal when an inactive (i.e., irrelevant) constraint is added to the problem. This property is 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 are presented. A straightforward test is described that concludes whether or not a BP is IIC.