  We show the existence of a fully polynomial-time approximation scheme (FPTAS)
for the problem of maximizing a non-negative polynomial over mixed-integer sets
in convex polytopes, when the number of variables is fixed. Moreover, using a
weaker notion of approximation, we show the existence of a fully
polynomial-time approximation scheme for the problem of maximizing or
minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes,
when the number of variables is fixed.
