Solving moment and polynomial optimization problems on Sobolev spaces
arxiv(2024)
摘要
Using standard tools of harmonic analysis, we state and solve the problem of
moments for positive 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 solve numerically non-convex polynomial optimization problems on
infinite-dimensional Sobolev spaces, with global convergence guarantees.
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