Houda Keraoui, Fatima Ezzahra Saissi, Abdelmalek Aboussoror, Stability and existence of solutions for weak bilevel optimization problems

Full Text: PDF
DOI: 10.23952/asvao.6.2024.2.04
Volume 6, Issue 2, 1 August 2024, Pages 179-192

Abstract. In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem $(S)$ in a topological sequential setting. To this aim, we consider an approach of $(S)$ by means of a family of regularized perturbed bilevel optimization problems $(S_n)$ of $(S)$ . Unlike $(S)$ , such problems $(S_n)$ have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem $(S)$ .

How to Cite this Article:
H. Keraoui, F.E. Saissi, A. Aboussoror, Stability and existence of solutions for weak bilevel optimization problems, Appl. Set-Valued Anal. Optim. 6 (2024), 179-192.