  In this paper, we introduce a kind of approximate Karush--Kuhn--Tucker
condition (AKKT) for a smooth cone-constrained vector optimization problem. We
show that, without any constraint qualification, the AKKT condition is a
necessary for a local weak efficient solution of the considered problem. For
convex problems, we prove that the AKKT condition is a necessary and sufficient
optimality condition for a global weak efficient solution. We also introduce
some strict constraint qualifications associated with the AKKT condition.
