Solving moment and polynomial optimization problems on Sobolev spaces
Optimization and Control
2025-07-08 v4
Abstract
Using standard tools of harmonic analysis, we state and solve the problem of moments for non-negative measures supported on the unit ball of a Sobolev space of multivariate periodic trigonometric functions. We describe outer and inner semidefinite approximations of the cone of Sobolev moments. They are the basic components of an infinite-dimensional moment-sums of squares hierarchy, allowing to numerically solve non-convex polynomial optimization problems on infinite-dimensional Sobolev spaces with global convergence guarantees
Keywords
Cite
@article{arxiv.2401.07734,
title = {Solving moment and polynomial optimization problems on Sobolev spaces},
author = {Didier Henrion and Alessandro Rudi},
journal= {arXiv preprint arXiv:2401.07734},
year = {2025}
}