STRONG-WEAK STACKELBERG PROBLEMS IN FINITE DIMENSIONAL SPACES

Abstract. We are concerned with two-level optimization problems called strong-weak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense. In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ǫ-approximate optimal solutions in the lower level problems. We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero. Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities. 1. Introduction and motivation. Let U and V be two finite dimensional Euclidean spaces, X (resp. Y) a nonempty subset of U (resp. of V). Let f1 and f2 b