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Pré-Publication, Document De Travail Année : 2022

Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials

Résumé

We consider the unconstrained optimization of multivariate trigonometric polynomials by the sum-of-squares hierarchy of lower bounds. We first show a convergence rate of O(1/s^2) for the relaxation with degree s without any assumption on the trigonometric polynomial to minimize. Second, when the polynomial has a finite number of global minimizers with invertible Hessians at these minimizers, we show an exponential convergence rate with explicit constants. Our results also apply to the minimization of regular multivariate polynomials on the hypercube.
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Dates et versions

hal-03843458 , version 1 (08-11-2022)
hal-03843458 , version 2 (12-12-2022)
hal-03843458 , version 3 (30-01-2023)
hal-03843458 , version 4 (16-04-2023)

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Francis Bach, Alessandro Rudi. Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials. 2022. ⟨hal-03843458v1⟩
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