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1706. Optimality and uniqueness of the D_4 root system
Invited abstract in session MC-38: Applications of polynomial optimization, stream Conic Optimization: Theory, Algorithms, and Applications.
Monday, 12:30-14:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Nando Leijenhorst
|
| Delft University of Technology | |
| 2. | David de Laat
|
| TU Delft | |
| 3. | Willem de Muinck Keizer
|
| Delft Institute of Applied Mathematics, TU Delft |
Abstract
The spherical code problem asks how to arrange N points on the unit sphere in dimension n such that the distance between the closest pair of points is maximized. We prove that for 24 points in dimension 4, the D_4 root system is the optimal configuration. We prove this by showing that it is the unique solution for the kissing number problem in dimension 4, up to isometry. For this we use a semidefinite programming relaxation of the the second step of the Lasserre hierarchy for spherical codes, for which we obtain an exact optimal solution by rounding the numerical solution using the techniques of [Cohn, de Laat, Leijenhorst, 2024+].
Keywords
- Convex Optimization
- Programming, Semidefinite
Status: accepted
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