Combined Reformulation of Bilevel Programming Problems

In J. J. Ye and D. L. Zhu proposed a new reformulation of a bilevel programming problem which compounds the value function and KKT approaches. In partial calmness condition was also adapted to this new reformulation and optimality conditions using partial calmness were introduced. In this paper we investigate above all local equivalence of the combined reformulation and the initial problem and how constraint qualifications and optimality conditions could be defined for this reformulation without using partial calmness. Since the optimal value function is in general nondifferentiable and KKT constraints have MPEC-structure, the combined reformulation is a nonsmooth MPEC. This special structure allows us to adapt some constraint qualifications and necessary optimality conditions from MPEC theory using disjunctive form of the combined reformulation. An example shows, that some of the proposed constraint qualifications can be fulfilled.