Minimizing the sum of many rational functions

Florian Bugarin (1, 2) , Didier Henrion (3) , Jean-Bernard Lasserre (3)

1 LAAS - Laboratoire d'analyse et d'architecture des systèmes
2 CROMeP - Centre de Recherche Outillages, Matériaux et Procédés
3 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande

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.

Mots clés: rational optimization; global optimization; semidefinite relaxations; sparsity

Domaines: Optimisation et contrôle [math.OC]

Florian Bugarin, Didier Henrion, Jean-Bernard Lasserre. Minimizing the sum of many rational functions. 2011. ⟨hal-00569067v1⟩