  An algorithm which computes a solution of a set optimization problem is
provided. The graph of the objective map is assumed to be given by finitely
many linear inequalities. A solution is understood to be a set of points in the
domain satisfying two conditions: the attainment of the infimum and minimality
with respect to a set relation. In the first phase of the algorithm, a linear
vector optimization problem, called the vectorial relaxation, is solved. The
resulting pre-solution yields the attainment of the infimum but, in general,
not minimality. In the second phase of the algorithm, minimality is established
by solving certain linear programs in combination with vertex enumeration of
some values of the objective map.
