Strongly Stable Stationary Points for a Class of Generalized Equations

Abstract

In this paper we consider a generalized equation that is mainly characterized by a cone-valued mapping. It is well known that optimality conditions for different classes of optimization problems can be formulated as such a generalized equation. Moreover, we generalize Kojima’s concept of strong stability and introduce appropriate constraint qualifications. We discuss corresponding properties between strong stability and these constraint qualifications. Finally, we apply these results to the particular class of mathematical programs with complementarity constraints and to that of mathematical programs with abstract constraints.