Abstract
In this paper, we are concerned with a weak (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).
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The authors are very grateful to the reviewers for useful suggestions and remarks which improved the quality of the paper.
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H.Keraoui, F.-E. Saissi and A.Aboussoror contributed equally in establishing the results of the manuscript; H.Keraoui drafted the manuscript; Supervision, F.-E. Saissi and A.Aboussoror; Validation, A.Aboussoror.
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Keraoui, H., Saissi, FE. & Aboussoror, A. On the Existence of Solutions for Weak Nonlinear Bilevel Optimization Problems. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00515-y
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DOI: https://doi.org/10.1007/s40305-023-00515-y