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Existence of solutions to weak nonlinear bilevel problems via minsup and d.c. problems. (English) Zbl 1151.49010

Summary: This is an extension of [A. Aboussoror and A. Mansouri, Sufficient conditions for minsup problems and application to bilevl programs, in: Proc. CIRO’05, IV Conf. Internationale en Recherche Opérationnelle. Théorie et Applications 1, 99–107 (2005)]. We first show the existence of solutions to a class of min-sup problems with linked constraints which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel problems. Furthermore, for such a class of bilevel problems, we give a relationship with appropriate d.c. problems concerning the existence of solutions.

MSC:

49J35 Existence of solutions for minimax problems
90C47 Minimax problems in mathematical programming
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
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References:

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