Math. Program., Ser. A (2012) 131:37–48 DOI 10.1007/s10107-010-0342-1 FULL LENGTH PAPER Is bilevel programming a special case of a mathematical program with complementarity constraints? S. Dempe · J. Dutta Received: 14 August 2008 / Accepted: 15 January 2010 / Published online: 25 February 2010 © Springer and Mathematical Programming Society 2010 Abstract Bilevel programming problems are often reformulated using the Karush– Kuhn–Tucker conditions for the lower level problem resulting in a mathematical pro- gram with complementarity constraints(MPCC). Clearly, both problems are closely related. But the answer to the question posed is “No” even in the case when the lower level programming problem is a parametric convex optimization problem. This is not obvious and concerns local optimal solutions. We show that global optimal solutions of the MPCC correspond to global optimal solutions of the bilevel problem provided the lower-level problem satisfies the Slater’s constraint qualification. We also show by examples that this correspondence can fail if the Slater’s constraint qualification fails to hold at lower-level. When we consider the local solutions, the relationship between the bilevel problem and its corresponding MPCC is more complicated. We also demonstrate the issues relating to a local minimum through examples. Keywords Bilevel programming · Mathematical programs with complementarity constraints · Optimality conditions · Local and global optimum Mathematics Subject Classification (2000) 90C30 1 Introduction Bilevel programming problems are hierarchical optimization problems combining decisions of two decision makers, the so-called leader and the so-called follower. S. Dempe (B ) Technical University Bergakademie Freiberg, Freiberg, Germany e-mail: dempe@tu-freiberg.de J. Dutta Indian Institute of Technology, Kanpur, India 123