Global optimization of rational multivariate functions

The paper deals with unconstrained global minimization of rational functions. A necessary condition is given for the function to have a finite infimum. In case the condition is satisfied, the problem is shown to be equivalent to a specific constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using semi-definite programming. In general, the relaxation will produce a lower bound of the infimum. However, under no degeneracies, it is possible to check whether the relaxation was in fact exact.