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
Kuhn-Tucker type necessary conditions for a point to be Pareto minimum
under the weaker constraint qualifications here proposed.