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

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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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     author = {Aboussoror, Abdelmalek and Mansouri, Abdelatif},
     title = {Existence of solutions to weak nonlinear bilevel problems via {MinSup} and d.c. problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {87--103},
     publisher = {EDP-Sciences},
     volume = {42},
     number = {2},
     year = {2008},
     doi = {10.1051/ro:2008012},
     mrnumber = {2431394},
     zbl = {1151.49010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro:2008012/}
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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, Tome 42 (2008) no. 2, pp. 87-103. doi: 10.1051/ro:2008012

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