Constraint Qualifications Revisited

In this study we investigate the constraint qualifications for the Kuhn-Tucker conditions to hold for an inequality-constrained nonlinear programming problem. We present the qualifications in a consistent manner so that the interrelationships between them are highlighted. This gives rise naturally to two types of constraint qualifications, and it will be seen that air the qualifications of one type are almost equally weak whereas the other type of qualifications makes relatively strong assumptions. In the study we also slightly relax the Kuhn-Tucker and some other constraint qualifications, and also show the interrelationship between some of the qualifications which have not been established thus far.