Stability and existence of solutions for weak bilevel optimization problems

. In this paper, we are interested in finding sufficient conditions, which ensure the existence of solutions to a weak (pessimistic) bilevel optimization problem ( S ) in a topological sequential setting. To this aim, we consider an approach of ( S ) by means of a family of regularized perturbed bilevel optimization problems ( S n ) of ( S ) . Unlike ( S ) , such problems ( S n ) have the privilege to admit solutions under mild assumptions. Using the notion of variational convergence, after establishing stability results, we prove the existence of solutions to problem ( S ) .