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Jennane, Mohsine; Kalmoun, El Mostafa; Lafhim, Lahoussine

Fuzzy and exact necessary optimality conditions for a nonsmooth bilevel semi-infinite program. (English) Zbl 07929249

Minimax Theory Appl. 9, No. 2, 305-324 (2024).
Summary: 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.

MSC:

90C46 Optimality conditions and duality in mathematical programming
49J52 Nonsmooth analysis
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics

Keywords:

parametric optimization; semi-infinite programming; optimality conditions; marginal and value functions; generalized differentiation; bilevel programming
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