2ND-ORDER CONDITIONS IN EXTREMAL PROBLEMS - THE ABNORMAL POINTS

In this paper we study a minimization problem with constraints and obt ain first- and second-order necessary conditions for a minimum. Those conditions - as opposed to the known ones - are also informative in th e abnormal case. We have introduced the class of 2-normal constraints and shown that for them the ''gap'' between the sufficient and the nec essary conditions is as minimal as possible. It is proved that a 2-nor mal mapping is generic.