Minimizing the sum of many rational functions

International audienceWe consider the problem of globally minimizing the sum of many rational functionsover 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 relatively large(10 to 100) provided some kind of sparsity is present. We describe a formulation of therational optimization problemas a generalized moment problem and its hierarchy of convex semidefinite relaxations. Undersome conditions we prove that the sequence of optimal values convergesto the globally optimal value. We show how public-domain software can beused to model and solve such problems. Finally, we also compare with the epigraph approach and the BARON software