An extension of the Basic Constraint Qualification to nonconvex vector optimization problems

In this paper a Basic Constraint Qualification is introduced for a nonconvex infinite‐dimensional vector optimization problem extending the usual one from convex programming assuming the Hadamard differentiability of the maps. Corresponding KKT conditions are established by considering a decoupling of the constraint cone into half‐spaces. This extension leads to generalized KKT conditions which are finer than the usual abstract multiplier rule. A second constraint qualification expressed directly in terms of the data is also introduced, which allows us to compute the contingent cone to the feasible set and, as a consequence, it is proven that this condition is a particular case of the first one. Relationship with other constraint qualifications in infinite‐dimensional vector optimization, specially with the Kurcyuscz‐Robinson‐Zowe constraint qualification, are also given.