CONVERGENCE RATES OF RLT AND LASSERRE-TYPE HIERARCHIES FOR THE GENERALIZED MOMENT PROBLEM OVER THE SIMPLEX AND THE SPHERE

Felix Kirschner (1) , Etienne de Klerk (1)

1 Tilburg University [Netherlands]

We consider the generalized moment problem (GMP) over the simplex and the sphere. This is a rich setting and it contains NP-hard problems as special cases, like constructing optimal cubature schemes and rational optimization. Using the Reformulation-Linearization Technique (RLT) and Lasserre-type hierarchies, relaxations of the problem are introduced and analyzed. For our analysis we assume throughout the existence of a dual optimal solution as well as strong duality. For the GMP over the simplex we prove a convergence rate of O(1/r) for a linear programming, RLT-type hierarchy, where r is the level of the hierarchy, using a quantitative version of Pólya's Positivstellensatz. As an extension of a recent result by Fang and Fawzi [Math.

Domaines: Mathématiques [math]

Felix Kirschner, Etienne de Klerk. CONVERGENCE RATES OF RLT AND LASSERRE-TYPE HIERARCHIES FOR THE GENERALIZED MOMENT PROBLEM OVER THE SIMPLEX AND THE SPHERE. 2021. ⟨hal-03170812⟩