- Exact semidefinite programming bounds for packing problems Maria Dostert(maria.dostertepfl.ch) David de Laat(d.delaattudelft.nl) Philippe Moustrou(philippe.moustrouuit.no) Abstract: In this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are unique up to rotations. In particular, we show that the configuration coming from the $E_8$ root lattice is the unique optimal code with minimal angular distance $\pi/3$ on the hemisphere in $\R^8$, and we prove that the three-point bound for the $(3, 8, \vartheta)$-spherical code, where $\vartheta$ is such that $\cos \vartheta = (\sqrt{8}-1)/7$, is sharp by rounding to $Q[\sqrt{8}]$. We also use our machinery to compute sharp upper bounds on the number of spheres that can be packed into a larger sphere. Keywords: semidefinite programming, spherical codes Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Citation: Download: [PDF]Entry Submitted: 01/03/2020Entry Accepted: 01/03/2020Entry Last Modified: 01/03/2020Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.