A parametric view on the Mangesarian–Fromovitz constraint qualification

In this paper we consider the behaviour of the multipliers for one-parametric semi-infinite programs near critical parameters, where the Mangasarian–Fromovitz constraint qualification can be violated. The growth of the multipliers, when the parameter approaches such a critical parameter, is characterized by a parametric constraint qualification which is introduced here. It is equivalent to a bound on the growth of the multipliers.