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We consider potentially non-convex optimization problems, for which optimalrates of approximation depend on the dimension of the parameter space and thesmoothness of the function to be optimized. In this paper, we propose analgorithm that achieves close to optimal a priori computational guarantees,while also providing a posteriori certificates of optimality. Our generalformulation builds on infinite-dimensional sums-of-squares and Fourieranalysis, and is instantiated on the minimization of multivariate periodicfunctions.

Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares