Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (4): 1048-1065.doi: 10.1007/s40305-023-00515-y

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On the Existence of Solutions for Weak Nonlinear Bilevel Optimization Problems

Houda Keraoui1,3, Fatima-Ezzahra Saissi2, Abdelmalek Aboussoror3   

  1. 1 Faculty of Sciences Semlalia, Laboratory of Mathematics and Population Dynamics, University of Cadi Ayyad, Marrakesh 40000, Morocco;
    2 National School of Applied Sciences of Berrechid Laboratory of Analysis and Modeling Systems for Decision Support, University of Hassan I, Berrechid 26100, Morocco;
    3 Faculty of Sciences Ben M'Sick Department of Mathematics and Computer Science, University of Hassan II, Casablanca 20645, Morocco
  • Received:2022-04-18 Revised:2023-08-30 Online:2025-12-30 Published:2025-12-19
  • Contact: Abdelmalek Aboussoror E-mail:aboussororabdel@hotmail.com

Abstract: 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).

Key words: Bilevel optimization, Variational convergence, Marginal functions, Limits of sets, Multifunctions

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