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

Published online by Cambridge University Press:  17 May 2008

Abdelmalek Aboussoror  and
Abdelatif Mansouri
Abdelmalek Aboussoror
Affiliation:
Université Cadi Ayyade, Faculté Polydisciplinaire de Safi, B.P. 4162, Safi, Morocco; aboussororabdel@hotmail.com
Abdelatif Mansouri
Affiliation:
Université Cadi Ayyad, Faculté des sciences Semlalia, Département de Mathématiques, B.P. 2390, Marrakech, Morocco; mansouri@ucam.ac.ma
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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 bilevelproblems. Furthermore, for such a class of bilevel problems, wegive a relationship with appropriate d.c. problems concerning theexistence of solutions.

Keywords

Min Sup problemsvariationalconvergencebilevel programmingd.c. programming.
Type
Research Article
Information
RAIRO - Operations Research , Volume 42 , Issue 2: CIRO 05 , April 2008 , pp. 87 - 103
Copyright
© EDP Sciences, ROADEF, SMAI, 2008

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