Work

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

Year: 2023

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2305.18768

Authors: Henrion, Didier, Infusino, Maria, Kuhlmann, Salma, Vinnikov, Victor

Institutions: Centre National de la Recherche Scientifique, Laboratoire d'Analyse et d'Architecture des Systèmes, Université de Toulouse, Czech Technical University in Prague, University of Cagliari, University of Konstanz, Ben-Gurion University of the Negev

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Baden-Württemberg Stiftung, Istituto Nazionale di Alta Matematica "Francesco Severi", Universität Konstanz, Mathematisches Forschungsinstitut Oberwolfach, Banff International Research Station for Mathematical Innovation and Discovery

OpenAlex ID: W4378942811

Cites: 28

Cited by: 1

Related to: 10