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

Autor:	Henrion, Didier, Infusino, Maria, Kuhlmann, Salma, Vinnikov, Victor
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Mathematics - Analysis of PDEs Mathematics - Functional Analysis Primary 90C25 Secondary 90C22 13J30 44A60 46N10 47A57
Druh dokumentu:	Working Paper
Popis:	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. Comment: 24 pages, 1 table, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.18768 Zobrazit plný text záznamu View this record from Arxiv