Minimax Theory and its Applications 09 (2024), No. 2, 305--324
Copyright Heldermann Verlag 2024
Fuzzy and Exact Necessary Optimality Conditions for a Nonsmooth Bilevel Semi-Infinite 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 so-called nonsmooth bilevel semi-infinite 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 Mangasarian-Fromovitz and Farkas-Minkowski CQs. We point out that the obtained results are new if we take up a finite number of constraints as well.
Keywords: Parametric optimization, semi-infinite programming, optimality conditions, marginal and value functions, generalized differentiation, bilevel programming.
MSC: 90C46, 49J52, 46N10.
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