On interval-valued bilevel optimization problems using upper convexificators

¹ Department of Mathematics and Computer Science, TU Bergakademie Freiberg, Freiberg, Germany
² LAMA, FSDM, Sidi Mohamed Ben Abdellah University, Fes, Morocco

^* Corresponding author: ohda.fsdm2021@gmail.com

Received: 24 February 2022
Accepted: 30 March 2023

Abstract

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.