Linear Bilevel Programming With Upper Level Constraints Depending on the Lower Level Solution Ayalew Getachew Mersha ∗ and Stephan Dempe † October 17, 2005 Abstract Focus in the paper is on the definition of linear bilevel programming problems, the existence of optimal solutions and necessary as well as sufficient optimality conditions. In the papers [9] and [10] the authors claim to suggest a refined definition of linear bilevel programming problems and related optimality conditions. Mainly their attempt reduces to shifting upper level constraints involving both the upper and the lower level variables into the lower level. We investigate such a shift in more details and show that it is not allowed in general. We show that an optimal solution of the bilevel programm exists under the conditions in [10] if we add the assumption that the inducible region is not empty. The necessary optimality condition reduces to check optimality in one linear programming problem. Optimality of one feasible point for a certain number of linear programs implies optimality for the bilevel problem. 1 Introduction The bilevel programming problem is an optimization problem whose con- straints are (in part) determined by an other optimization problem. In other words it is an hierarchical optimization problem consisting of two levels, the * Department of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Germany † Department of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Germany 1