Solving moment and polynomial optimization problems on Sobolev spaces

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

References in corpus (5)

• Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
• The A-truncated K-moment problem
• The full infinite dimensional moment problem on semi-algebraic sets of generalized functions
• An intrinsic characterization of moment functionals in the compact case
• Moment problem for algebras generated by a nuclear space