ABSTRACT
Until now we have studied how to derive the necessary KKT optimality conditions for convex programming problems (CP ) or its slight variations such as (CP1), (CCP ) or (CCP1) via normal cone or saddle point approach. Observe that in the KKT optimality conditions, the multiplier associated with the subdifferential of the objective function is nonzero and thus normalized to one. As discussed in Chapters 3 and 4, some additional conditions known as the constraint qualifications are to be satisfied by the constraints to ensure that the multiplier is nonzero and hence the KKT optimality conditions hold. But in absence a of constraint qualification, one may not be able to derive KKT optimality conditions. For example, consider the problem
min x subject to x2 ≤ 0.
