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Pré-Publication, Document De Travail Année : 2023

Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations

Résumé

We formulate a class of nonlinear evolution partial differential equations (PDEs) as linear optimization problems on moments of positive measures supported on infinite-dimensional vector spaces. Using sums of squares (SOS) representations of polynomials in these spaces, we can prove convergence of a hierarchy of finite-dimensional semidefinite relaxations solving approximately these infinite-dimensional optimization problems. As an illustration, we report on numerical experiments for solving the heat equation subject to a nonlinear perturbation.
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hal-04117218 , version 1 (05-06-2023)

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Didier Henrion, Maria Infusino, Salma Kuhlmann, Victor Vinnikov. Infinite-dimensional moment-SOS hierarchy for nonlinear partial differential equations. 2023. ⟨hal-04117218⟩
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