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 nite innmum. In case the condition is satissed, the problem is shown to be equivalent to a speciic constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using semi-deenite programming. In general, the relaxation will produce a lower bound of the innmum. However, under no degeneracies, it is possible to check whether the relaxation was in fact exact.