Corpus ID: 209531959

Exact semidefinite programming bounds for packing problems

@article{Dostert2020ExactSP,
  title={Exact semidefinite programming bounds for packing problems},
  author={M. Dostert and David de Laat and Philippe Moustrou},
  journal={arXiv: Optimization and Control},
  year={2020}
}
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 $\mathsf{E}_8$ root lattice is the unique optimal code with minimal angular distance… Expand
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