  In the present paper, we are concerned with a class of constrained vector
optimization problems, where the objective functions and active constraint
functions are locally Lipschitz at the referee point. Some second-order
constraint qualifications of Zangwill type, Abadie type and
Mangasarian~--~Fromovitz type as well as a regularity condition of Abadie type
are proposed in a nonsmooth setting. The connections between these proposed
conditions are established. They are applied to develop second-order
Karush--Kuhn--Tucker necessary optimality conditions for local (weak, Geoffrion
properly) efficient solutions to the considered problem. Examples are also
given to illustrate the obtained results.
