In this paper, we investigate a bilevel interval valued optimization problem. Reducing the problem into a one-level nonlinear and nonsmooth program, necessary optimality conditions are developed in terms of upper convexificators. Our approach consists of using an Abadie’s constraint qualification together with an appropriate optimal value reformulation. Later on, using an upper estimate for upper convexificators of the optimal value function, we give a more detailed result in terms of the initial data. The appearing functions are not necessarily Lipschitz continuous, and neither the objective function nor the constraint functions of the lower-level optimization problem are assumed to be convex. There are additional examples highlighting both our results and the limitations of certain past studies.

This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given.

No abstract

No abstract

<p style='text-indent:20px;'>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.</p>