Weak Nonlinear Bilevel Problems : Existence of Solutions via Reverse Convex and Convex Maximization Problems

Abdelmalek Aboussoror , Samir Adly (1) , Vincent Jalby (1)

1 DMI

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.

Mots clés: reverse convex programs; d.c. programs; two-level optimization; convex analysis

Domaines: Optimisation et contrôle [math.OC]

Abdelmalek Aboussoror, Samir Adly, Vincent Jalby. Weak Nonlinear Bilevel Problems : Existence of Solutions via Reverse Convex and Convex Maximization Problems. Journal of Industrial and Management Optimization, 2011, 7 (3), pp.559-571. ⟨10.3934/jimo.2011.7.559⟩. ⟨hal-00682742⟩