  This paper is concerned with solution algorithms for general convex vector
optimization problems (CVOPs). So far, solution concepts and approximation
algorithms for solving CVOPs exist only for bounded problems [Ararat et al.
2022, Doerfler et al. 2021, Loehne et al. 2014]. They provide a polyhedral
inner and outer approximation of the upper image that have a Hausdorff distance
of at most $\varepsilon$. However, it is well known (see [Ulus, 2018]), that
for some unbounded problems such polyhedral approximations do not exist. In
this paper, we will propose a generalized solution concept, called an
$(\varepsilon,\delta)$--solution, that allows also to consider unbounded CVOPs.
It is based on additionally bounding the recession cones of the inner and outer
polyhedral approximations of the upper image in a meaningful way. An algorithm
is proposed that computes such $\delta$--outer and $\delta$--inner
approximations of the recession cone of the upper image. In combination with
the results of [Loehne et al. 2014] this provides a primal and a dual algorithm
that allow to compute $(\varepsilon,\delta)$--solutions of (potentially
unbounded) CVOPs. Numerical examples are provided.
