Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems
RAIRO - Operations Research - Recherche Opérationnelle, Volume 42 (2008) no. 2, pp. 87-103.

In this paper, which is an extension of [4], 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.

DOI: 10.1051/ro:2008012
Classification: 49K35, 90C47, 91A44, 46N10
Keywords: $\operatorname{Min}\operatorname{Sup}$ problems, variational convergence, bilevel programming, d.c. programming
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Aboussoror, Abdelmalek; Mansouri, Abdelatif. Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems. RAIRO - Operations Research - Recherche Opérationnelle, Volume 42 (2008) no. 2, pp. 87-103. doi : 10.1051/ro:2008012. http://archive.numdam.org/articles/10.1051/ro:2008012/

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