Necessary Conditions for Bilevel Multiobjective Programming Problems

In this paper, the necessary conditions for bilevel multiobjective programming problems are discussed. Assuming the upper-level objective functions in bilevel multiobjective programming problems are differentiable, we give and prove its first-order necessary conditions of the weak (strong) minimizer by applying the concept and properties of the contingent epiderivative for set-valued maps. The obtained necessary conditions are formed by the gradients of the upper-level objective functions and the contingent epiderivative of the efficient points set for the lower-level problems of optimization.