  In one of our earlier works, we proposed to approximate Pareto fronts to
multiobjective optimization problems by two-sided approximations, one from
inside and another from outside of the feasible objective set, called,
respectively, lower shell and upper shell. We worked there under the assumption
that for a given problem an upper shell exists. As it is not always the case,
in this paper we give some sufficient conditions for the existence of upper
shells.
  We also investigate how to constructively search infeasible sets to derive
upper shells. We approach this issue by means of problem relaxations. We
formally show that under certain conditions some subsets of lower shells to
relaxed multiobjective optimization problems are upper shells in the respective
unrelaxed problems.
  Results presented are illustrated by a numerical example representing a~small
but real mechanical problem. Practical implications of the results are
discussed.
