Rigidity of abnormal extrema in the problem of non-linear programming with mixed constraints

Abstract

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.