  A bilevel program is an optimization problem whose constraints involve
another optimization problem. This paper studies bilevel polynomial programs
(BPPs), i.e., all the functions are polynomials. We reformulate BPPs
equivalently as semi-infinite polynomial programs (SIPPs), using Fritz John
conditions and Jacobian representations. Combining the exchange technique and
Lasserre type semidefinite relaxations, we propose numerical methods for
solving both simple and general BPPs. For simple BPPs, we prove the convergence
to global optimal solutions. Numerical experiments are presented to show the
efficiency of proposed algorithms.
