Second-order conditions in extremal problems. The abnormal points
Aram Vladimirovich Arutyunov · Transactions of the American Mathematical Society · 1998
In this paper we study a minimization problem with constraints and obtain first- and second-order necessary conditions for a minimum. Those conditions – as opposed to the known ones – are also informative in the abnormal case. We have introduced the class of 2-normal constraints and shown that for them the “gap" between the sufficient and the necessary conditions is as minimal as possible. It is proved that a 2-normal mapping is generic.