Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube
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| Title: | Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube |
|---|---|
| Authors: | Gribling, Sander, de Klerk, Etienne, Vera, Juan |
| Publication Year: | 2025 |
| Collection: | ArXiv.org (Cornell University Library) |
| Subject Terms: | Optimization and Control |
| Description: | We revisit the problem of minimizing a given polynomial $f$ on the hypercube $[-1,1]^n$. Lasserre's hierarchy (also known as the moment- or sum-of-squares hierarchy) provides a sequence of lower bounds $\{f_{(r)}\}_{r \in \mathbb N}$ on the minimum value $f^*$, where $r$ refers to the allowed degrees in the sum-of-squares hierarchy. A natural question is how fast the hierarchy converges as a function of the parameter $r$. The current state-of-the-art is due to Baldi and Slot [SIAM J. on Applied Algebraic Geometry, 2024] and roughly shows a convergence rate of order $1/r$. Here we obtain closely related results via a different approach: the polynomial kernel method. We also discuss limitations of the polynomial kernel method, suggesting a lower bound of order $1/r^2$ for our approach. ; 24 pages, 3 figures |
| Document Type: | text |
| Language: | unknown |
| Relation: | http://arxiv.org/abs/2505.00544 |
| Availability: | http://arxiv.org/abs/2505.00544 |
| Accession Number: | edsbas.AA21A4E4 |
| Database: | BASE |
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