Rigidity of abnormal extrema in nonlinear programming problems with equality and inequality constraints

Optimality conditions for nonlinear problems with equality and inequality constraints are considered. In the case when no constraint qualification (or regularity) is assumed, the Lagrange multiplier corresponding to the objective function can vanish in first order necessary optimality conditions given by Fritz John and the corresponding extremum is called abnormal. In the paper we consider second order sufficient optimality conditions that guarantee the rigidity of abnormal extrema (i.e. their isolatedness in the admissible sets).