  The object of investigation in this paper are vector nonlinear programming
problems with cone constraints. We introduce the notion of a Fritz John
pseudoinvex cone-constrained vector problem. We prove that a problem with cone
constraints is Fritz John pseudoinvex if and only if every vector critical
point of Fritz John type is a weak global minimizer. Thus, we generalize
several results, where the Paretian case have been studied.
  We also introduce a new Frechet differentiable pseudoconvex problem. We
derive that a problem with quasiconvex vector-valued data is pseudoconvex if
and only if every Fritz John vector critical point is a weakly efficient global
solution. Thus, we generalize a lot of previous optimality conditions,
concerning the scalar case and the multiobjective Paretian one.
  Additionally, we prove that a quasiconvex vector-valued function is
pseudoconvex with respect to the same cone if and only if every vector critical
point of the function is a weak global minimizer, a result, which is a natural
extension of a known characterization of pseudoconvex scalar functions.
