Constraint qualifications and KKT conditions for bilevel programming problems

In this paper we consider the bilevel programming problem (BLPP), which is a sequence of two optimization problems where the constraint region of the upper–level problem is determined implicitly by the solution set to the lower–level problem. We extend well–known constraint qualifications for nonlinear programming problems such as the Abadie constraint qualification, the Kuhn–Tucker constraint qualification, the Zangwill constraint qualification, the Arrow–Hurwicz–Uzawa constraint qualification, and the weak reverse convex constraint qualification to BLPPs and derive a Karash–Kuhn–Tucker (KKT)–type necessary optimality condition under these constraint qualifications without assuming the lower–level problem satisfying the Mangasarian Fromovitz constraint qualification. Relationships among various constraint qualifications are also given.