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, Mathematical Programming Computation, 2024, 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:2403.16874
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]
- N. Leijenhorst and D. de Laat. Solving clustered low-rank semidefinite programs arising from polynomial optimization. Mathematical Programming Computation 16, 503–534 (2024), arXiv:2202.12077.
- [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).