RAIRO-Oper. Res. 42 (2008) 87-103
DOI: 10.1051/ro:2008012

Existence of solutions to weak nonlinear bilevel problems via MinSup and d.c. problems

Abdelmalek Aboussoror¹ and Abdelatif Mansouri<sup>2

1</sup>  Université Cadi Ayyade, Faculté Polydisciplinaire de Safi, B.P. 4162, Safi, Morocco; aboussororabdel@hotmail.com
²  Université Cadi Ayyad, Faculté des sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakech, Morocco; mansouri@ucam.ac.ma

(Received September 1, 2006. Accepted November 11, 2007 Published online 17 May 2008.)

Abstract
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.

Mathematics Subject Classification. 49K35, 90C47, 91A44, 46N10.

Key words: problems, variational convergence, bilevel programming, d.c. programming.


© EDP Sciences, ROADEF, SMAI 2008