  The problem of minimizing the difference of two convex functions is called
polyhedral d.c. optimization problem if at least one of the two component
functions is polyhedral. We characterize the existence of global optimal
solutions of polyhedral d.c. optimization problems. This result is used to show
that, whenever the existence of an optimal solution can be certified,
polyhedral d.c. optimization problems can be solved by certain concave
minimization algorithms. No further assumptions are necessary in case of the
first component being polyhedral and just some mild assumptions to the first
component are required for the case where the second component is polyhedral.
In case of both component functions being polyhedral, we obtain a primal and
dual existence test and a primal and dual solution procedure. Numerical
examples are discussed.
