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Convergence of Lasserre's hierarchy: the general case

Matteo Tacchi 1
1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : Lasserre's moment-SOS hierarchy consists of approximating instances of the generalized moment problem (GMP) with moment relaxations and sums-of-squares (SOS) strenghtenings that boil down to convex semidefinite programming (SDP) problems. Due to the generality of the initial GMP, applications of this technology are countless, and one can cite among them the polynomial optimization problem (POP), the optimal control problem (OCP), the volume computation problem, stability sets approximation problems, and solving nonlinear partial differential equations (PDE). The solution to the original GMP is then approximated with finite truncatures of its moment sequence. For each application , proving convergence of these truncatures towards the optimal moment sequence gives valuable insight on the problem, including convergence of the relaxed values to the original GMP's optimal value. This note proposes a general proof of such convergence, regardless the problem one is faced with, under simple standard assumptions. As a byproduct of this proof, one also obtains strong duality properties both in the infinite dimensional GMP and its finite dimensional relaxations.
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Contributor : Matteo Tacchi <>
Submitted on : Monday, November 16, 2020 - 6:47:38 PM
Last modification on : Wednesday, November 18, 2020 - 4:30:12 PM


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  • HAL Id : hal-03008545, version 1


Matteo Tacchi. Convergence of Lasserre's hierarchy: the general case. 2020. ⟨hal-03008545⟩



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