  There are different solution concepts for convex vector optimization problems
(CVOPs) and a recent one, which is motivated from a set optimization point of
view, consists of finitely many efficient solutions that generate polyhedral
inner and outer approximations to the Pareto frontier. A CVOP with compact
feasible region is known to be bounded and there exists a solution of this
sense to it. However, it is not known if it is possible to generate polyhedral
inner and outer approximations to the Pareto frontier of a CVOP if the feasible
region is not compact. This study shows that not all CVOPs are tractable in
that sense and gives a characterization of tractable problems in terms of the
well known weighted sum scalarization problems.
