In this paper,we are concernedwith aweak(pessimistic) nonlinear bilevel optimization problem. In a sequential setting, for such a problem, we provide sufficient conditions ensuring the existence of solutions via a regularization and the notion of variational convergence. Unlike the approaches adopted by Aboussoror and Loridan (J Math Anal Appl 254: 348-357, 2001) and Aboussoror (Adv Math Res 1: 83-92, 2002), our approach does not require convexity assumptions and gives an extension from the finite dimensional case to a general topological one. Moreover, it gives an improvement of the result given by Loridan and Morgan (in: Buhler et al. (ed) Operations Research Proceedings of the international Conference on Operations Research 90 in Vienna, Springer Verlag, Berlin 1992).
Houda Keraoui, Fatima-Ezzahra Saissi, Abdelmalek Aboussoror
. On the Existence of Solutions for Weak Nonlinear Bilevel Optimization Problems[J]. Journal of the Operations Research Society of China, 2025
, 13(4)
: 1048
-1065
.
DOI: 10.1007/s40305-023-00515-y
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