Solving moment and polynomial optimization problems on Sobolev spaces

  • Didier Henrion
  • Alessandro Rudi
    • Categories Global Optimization, Infinite Dimensional Optimization, Semi-definite Programming Tags , , , Short URL: https://optimization-online.org/?p=25373

    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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