References and citing

The semidefinite programming solver and the interface (including sampled polynomials) in ClusteredLowRankSolver.jl have been developed as part of the paper

Nando Leijenhorst and David de Laat, Solving clustered low-rank semidefinite programs arising from polynomial optimization, preprint, 2022. arXiv:2202.12077

The solver was inspired by the more specialized solver

David Simmons-Duffin. A semidefinite program solver for the conformal bootstrap. J. High Energy Phys. 174 (2015), arXiv:1502.02033

The rounding procedure in ClusteredLowRankSolver.jl has been developed as part of the paper

Henry Cohn, David de Laat, and Nando Leijenhorst, Optimality of spherical codes via exact semidefinite programming bounds, preprint, 2024. arXiv:???

This improves the rounding procedure developed in

Maria Dostert, David de Laat, and Philippe Moustrou, Exact semidefinite programming bounds for packing problems, SIAM J. Optim. 31(2) (2021), 1433-1458, arXiv:2001.00256

References

[1]: H. Cohn, D. de Laat and N. Leijenhorst. Optimality of spherical codes via exact semidefinite programming bounds, arXiv:2403.16874 (2024).
[2]: D. de Laat and N. Leijenhorst. Solving clustered low-rank semidefinite programs arising from polynomial optimization, arXiv:2202.12077 (2022).
[3]: D. Simmons-Duffin. A semidefinite program solver for the conformal bootstrap. Journal of High Energy Physics 2015, 174 (2015).
[4]: P. Delsarte, J. M. Goethals and J. J. Seidel. Spherical codes and designs. Geometriae Dedicata 6, 363–388 (1977).
[5]: D. de Laat, F. M. de Oliveira Filho and F. Vallentin. Upper bounds for packings of spheres of several radii. Forum of Mathematics, Sigma 2, e23 (2014).
[6]: H. Cohn and N. Elkies. New upper bounds on sphere packings. I. Annals of Mathematics (2) 157, 689–714 (2003).
[7]: K. Gatermann and P. A. Parrilo. Symmetry groups, semidefinite programs, and sums of squares. Journal of Pure and Applied Algebra 192, 95–128 (2004).