On multiobjective bilevel optimization using tangential subdifferentials

Multiobjective optimization problems typically have conflicting objectives, and a gain in one objective very often is an expense in another. In this paper, we investigate a multiobjective bilevel optimization problem. Using the concept of efficiency together with the optimal value reformulation, we give necessary optimality conditions in terms of tangential subdifferentials. Completely detailed first-order necessary optimality conditions are then derived in the special case where the lower level problem is convex. An example that illustrates our findings is also given.