Geodesic
Fuzzy and Exact Necessary Optimality Conditions for a Nonsmooth Bilevel Semi-Infinite Program
Minimax theory and its applications, Tome 9 (2024) no. 2
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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.
Mots-clés : Parametric optimization, semi-infinite programming, optimality conditions, marginal and value functions, generalized differentiation, bilevel programming 
@article{MTA_2024_9_2_a8,
     author = {Mohsine Jennane and El Mostafa Kalmoun,Lahoussine Lafhim},
     title = {Fuzzy and {Exact} {Necessary} {Optimality} {Conditions} for a {Nonsmooth} {Bilevel} {Semi-Infinite} {Program}},
     journal = {Minimax theory and its applications},
     year = {2024},
     volume = {9},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a8/}
}
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Mohsine Jennane; El Mostafa Kalmoun,Lahoussine Lafhim. Fuzzy and Exact Necessary Optimality Conditions for a Nonsmooth Bilevel Semi-Infinite Program. Minimax theory and its applications, Tome 9 (2024) no. 2. http://geodesic.mathdoc.fr/item/MTA_2024_9_2_a8/