  This paper considers the optimization problem of minimizing a rational
function. We reformulate this problem as polynomial optimization by the
technique of homogenization. These two problems are shown to be equivalent
under some generic conditions. The exact Jacobian SDP relaxation method
proposed by Nie is used to solve the resulting polynomial optimization. We also
prove that the assumption of nonsingularity in Nie's method can be weakened as
the finiteness of singularities. Some numerical examples are given to
illustrate the efficiency of our method.
