  In this paper, we consider a bilevel polynomial optimization problem where
the objective and the constraint functions of both the upper and the lower
level problems are polynomials. We present methods for finding its global
minimizers and global minimum using a sequence of semidefinite programming
(SDP) relaxations and provide convergence results for the methods. Our scheme
for problems with a convex lower-level problem involves solving a transformed
equivalent single-level problem by a sequence of SDP relaxations; whereas our
approach for general problems involving a non-convex polynomial lower-level
problem solves a sequence of approximation problems via another sequence of SDP
relaxations.
