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Zbl 1151.49010
Aboussoror, Abdelmalek; Mansouri, Abdelatif
Existence of solutions to weak nonlinear bilevel problems via minsup and d.c. problems. (English)
[J] RAIRO, Oper. Res. 42, No. 2, 87-102 (2008). ISSN 0399-0559; ISSN 1290-3868/e

Summary: This is an extension of [{\it A. Aboussoror} and {\it 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 2000:: *49J35 Minimax problems (existence)
90C47 Minimax problems
46N10 Appl. of functional analysis in optimization and math. programming

Keywords: min-sup problems; variational convergence; bilevel programming; d.c. programming

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