Solving moment and polynomial optimization problems on Sobolev spaces

Didier Henrion; Alessandro Rudi

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arXiv · 2401.07734

Solving moment and polynomial optimization problems on Sobolev spaces

Didier Henrion·Alessandro Rudi

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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

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Didier Henrion, Alessandro Rudi. 2024-01-15. Solving moment and polynomial optimization problems on Sobolev spaces. https://arxiv.org/abs/2401.07734

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