We study abnormal extremum in the problem of non-linear pro-
gramming with mixed constraints. Abnormal extremum occurs when
in necessary optimality conditions the Lagrange multiplier, which cor-
responds to the objective function, vanishes. We demonstrate that in
this case abnormal second-order su±cient optimality conditions guar-
antee rigidity of the corresponding extremal point, which means iso-
latedness of this point in the set determined by the constraints
