On constraint qualifications in directionally differentiable multiobjective optimization problems

We consider a multiobjective optimization problem with a feasible set defined by inequality and equality constraints such that all functions are, at least, Dini differentiable (in some cases, Hadamard differentiable and sometimes, quasiconvex). Several constraint qualifications are given in such a way that generalize both the qualifications introduced by Maeda and the classical ones, when the functions are differentiable. The relationships between them are analyzed. Finally, we give several Karush–Kuhn–Tucker type necessary conditions for a point to be Pareto minimum under the weaker constraint qualifications here proposed.