  We propose an algorithm to generate inner and outer polyhedral approximations
to the upper image of a bounded convex vector optimization problem. It is an
outer approximation algorithm and is based on solving norm minimizing
scalarizations. Unlike Pascolleti-Serafini scalarization used in the literature
for similar purposes, it does not involve a direction parameter. Therefore, the
algorithm is free of direction-biasedness. We also propose a modification of
the algorithm by introducing a suitable compact subset of the upper image,
which helps in proving for the first time the finiteness of an algorithm for
convex vector optimization. The computational performance of the algorithms is
illustrated using some of the benchmark test problems, which shows promising
results in comparison to a similar algorithm that is based on
Pascoletti-Serafini scalarization.
