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Article Dans Une Revue SIAM Journal on Optimization Année : 2023

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

Francis Bach
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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 minimizing 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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Citer

Francis Bach, Alessandro Rudi. Exponential convergence of sum-of-squares hierarchies for trigonometric polynomials. SIAM Journal on Optimization, In press, ⟨10.1137/22m1540818⟩. ⟨hal-03843458v4⟩
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