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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.
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A. V. Arutyunov (1998) studied this question.
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