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Watch this 36-minute conference talk by Didier Henrion of the Centre National de la Recherche Scientifique (CNRS) recorded on May 21, 2025, at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop. Explore how standard tools of harmonic analysis can be applied to 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. Learn about outer and inner semidefinite approximations of the cone of Sobolev moments and how they function as basic components of an infinite-dimensional moment-sums of squares hierarchy. Discover numerical methods for solving non-convex polynomial optimization problems on infinite-dimensional Sobolev spaces with global convergence guarantees.
