Strong-weak nonlinear bilevel problems : existence of solutions in a sequential setting

par Fatima Ezzahra Saissi (Université de Limoges)

vendredi 30 janv. 2015, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

In this talk, we are concerned with a strong-weak nonlinear bilevel problem which generalizes the well-studied weak and strong ones. As it is well-known, weak bilevel problems are difficult to solve from both theoretical and numerical aspects. Due to this generalization, strong-weak bilevel problems present more difficulties. In particular, the study of the existence of solutions is a very difficult task. For such a problem, we first give a regularization based on the use of strict epsilon-solutions of the lower level problem. Via this regularization, we have given sufficient conditions ensuring the existence of solutions to the strong-weak bilevel problem. One of the sufficient conditions reduces the problem of the existence of solutions to a problem of the existence of a common solution of two parametrized one-level optimization problems. Therefore, our investigation led us to a study in one-level optimization.