  An application area of vertex enumeration problem (VEP) is the usage within
objective space based linear/convex {vector} optimization algorithms whose aim
is to generate (an approximation of) the Pareto frontier. In such algorithms,
VEP, which is defined in the objective space, is solved in each iteration and
it has a special structure. Namely, the recession cone of the polyhedron to be
generated is the {ordering} cone. We {consider and give a detailed description
of} a vertex enumeration procedure, which iterates by calling a modified
`double description (DD) method' that works for such unbounded polyhedrons. We
employ this procedure as a function of an existing objective space based
{vector} optimization algorithm (Algorithm 1); and test the performance of it
for randomly generated linear multiobjective optimization problems. We compare
the efficiency of this procedure with another existing DD method as well as
with the current vertex enumeration subroutine of Algorithm 1. We observe that
the modified procedure excels the others especially as the dimension of the
vertex enumeration problem (the number of objectives of the corresponding
multiobjective problem) increases.
