Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913174100377600 |
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| author | Gribling, Sander de Klerk, Etienne Vera, Juan C. |
| author_facet | Gribling, Sander de Klerk, Etienne Vera, Juan C. |
| contents | We propose a new family of polynomial approximation kernels for approximating nonnegative polynomials on the hypercube $[-1,1]^n$. Our Kernels produce polynomial sums-of-squares of degree $r$, achieving an $O(\log^3 r/r^2)$ error in the $\ell_1$-norm of the coefficients. This improves on the known error bound $O(1/r)$ from the literature. As a corollary, we obtain an improved convergence rate for the Lasserre hierarchy for polynomial optimization on the hypercube, again improving a known rate by Baldi and Slot from $O(1/r)$ to $O(\log^3 r/r^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31496 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies Gribling, Sander de Klerk, Etienne Vera, Juan C. Optimization and Control We propose a new family of polynomial approximation kernels for approximating nonnegative polynomials on the hypercube $[-1,1]^n$. Our Kernels produce polynomial sums-of-squares of degree $r$, achieving an $O(\log^3 r/r^2)$ error in the $\ell_1$-norm of the coefficients. This improves on the known error bound $O(1/r)$ from the literature. As a corollary, we obtain an improved convergence rate for the Lasserre hierarchy for polynomial optimization on the hypercube, again improving a known rate by Baldi and Slot from $O(1/r)$ to $O(\log^3 r/r^2)$. |
| title | Squared polynomial approximation kernels for the hypercube: improved error bounds and implications for Lasserre hierarchies |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.31496 |