A hierarchy of convex relaxations for the total variation distance
Résumé
Given two measures µ, ν on Rd that satisfy Carleman's condition, we provide a numerical scheme to approximate as closely as desired the total variation distance between µ and ν. It consists of solving a sequence (hierarchy) of convex relaxations whose associated sequence of optimal values converges to the total variation distance, an additional illustration of the versatility of the Moment-SOS hierarchy. Indeed each relaxation in the hierarchy is a semidefinite program whose size increases with the number of involved moments. It has an optimal solution which is a couple of degree-2n pseudo-moments which converge, as n grows, to moments of the Hahn-Jordan decomposition of µ-ν.
Domaines
Optimisation et contrôle [math.OC]| Origine | Fichiers produits par l'(les) auteur(s) |
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