
Minimax Theory and its Applications 09 (2024), No. 2, 305324 Copyright Heldermann Verlag 2024 Fuzzy and Exact Necessary Optimality Conditions for a Nonsmooth Bilevel SemiInfinite Program Mohsine Jennane FSDM, Dept. of Mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco mohsine.jennane@usmba.ac.ma El Mostafa Kalmoun School of Science and Engineering, Al Akhawayn University, Ifrane, Morocco e.kalmoun@aui.ma Lahoussine Lafhim FSDM, Dept. of Mathematics, Sidi Mohamed Ben Abdellah University, Fez, Morocco lahoussine.lafhim@usmba.ac.ma We investigate the socalled nonsmooth bilevel semiinfinite programming problem when the involved functions are nonconvex. This type of problems consists of an infinite number of constraints with arbitrary index sets. To establish the optimality conditions, we rewrite upper estimates of three recently developed subdifferentials of the value functions using two new qualification conditions (CQs), which are weaker than the existing MangasarianFromovitz and FarkasMinkowski CQs. We point out that the obtained results are new if we take up a finite number of constraints as well. Keywords: Parametric optimization, semiinfinite programming, optimality conditions, marginal and value functions, generalized differentiation, bilevel programming. MSC: 90C46, 49J52, 46N10. [ Fulltextpdf (173 KB)] for subscribers only. 