Second–order Conditions in Extremal Problems. the Abnormal Points

@inproceedings{Arutyunov1998SecondorderCI,
  title={Second–order Conditions in Extremal Problems. the Abnormal Points},
  author={Aram V. Arutyunov},
  year={1998}
}
In this paper we study a minimization problem with constraints and obtain firstand 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. 
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