Coderivatives with Respect to a Set of the Normal Cone Mappings and Their Applications

Abstract. Establishing explicit formulas of coderivatives with respect to a set of the normal cone mapping to a polyhedron, the solution set of a variational inequality system, is one of the main goals of this paper. By using our coderivative formulas, we provide a characteristic of the Aubin property with respect to a set of that normal cone mapping and then give necessary optimality conditions for simple bilevel optimization problems under weak qualification conditions.