Sensitivity Analysis for Two-Level Value Functions with Applications to Bilevel Programming

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization called the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not---to a large extent---differ from those known for the conventional problem. It has already been well recognized in the literature that for optimality conditions of the usual optimistic bilevel program appropriate coderivative constructions for the set-valued solution map of the lower-level problem could be used, while it is shown in this paper that for the original optimistic formulation we have to go a step further to require and justify a certain Lipschitz-like property of this map. This is related to the local Lipschitz continuity of the optimal value funct...