  We consider the problem of globally minimizing the sum of many rational
functions over a given compact semialgebraic set. The number of terms can be
large (10 to 100), the degree of each term should be small (up to 10), and the
number of variables can be large (10 to 100) provided some kind of sparsity is
present. We describe a formulation of the rational optimization problem as a
generalized moment problem and its hierarchy of convex semidefinite
relaxations. Under some conditions we prove that the sequence of optimal values
converges to the globally optimal value. We show how public-domain software can
be used to model and solve such problems.
