Second-order necessary optimality conditions for problems without a priori normality assumptions

In this article, we derive second–order necessary conditions of optimality for an abstract optimization problem with equality and inequality constraints and constraints in the form of an inclusion into a given closed set. An important feature is that our optimality conditions dispense with any a priori normality assumptions, such as Robinson's constraint qualification, and remain informative even for abnormal points. Moreover, our optimality conditions take into account the second–order effect of the curvature of the set in the inclusion constraints.