Weak nonlinear bilevel problems: Existence of solutions via reverse convex and convex maximization problems

Abdelmalek Aboussoror; Samir Adly; Vincent Jalby

doi:10.3934/jimo.2011.7.559

Article Contents

2011, Volume 7, Issue 3: 559-571. Doi: 10.3934/jimo.2011.7.559

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Weak nonlinear bilevel problems: Existence of solutions via reverse convex and convex maximization problems

1.
Université Cadi Ayyad, Faculté Polydisciplinaire de Saﬁ, B.P. 4162, Sidi Bouzid, Saﬁ
2.
Laboratoire XLIM UMR-CNRS 6172, Université de Limoges Département de Mathématiques, 123 Avenue Albert Thomas 87060 Limoges Cedex

Received: June 30, 2010

Revised: February 28, 2011

Published: June 2011

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Abstract

In this paper, for a class of weak bilevel programming problems we provide sufficient conditions guaranteeing the existence of global solutions. These conditions are based on the use of reverse convex and convex maximization problems.

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Mathematics Subject Classification: 91A65, 90C26, 52A41.

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References

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