1495. Obtuse almost-equiangular sets
Invited abstract in session WD-49: Advances in Conic Optimization and Applications, stream Conic and polynomial optimization.
Wednesday, 14:30-16:00Room: Parkinson B10
Authors (first author is the speaker)
| 1. | Bram Bekker
|
| DIAM, Delft University of Technology |
Abstract
For t between -1 and 1, a set of points on the (n−1)-dimensional unit sphere is called t-almost equiangular if among any three distinct points there is a pair with inner product t. We propose a semidefinite programming upper bound for the maximum cardinality α(n,t) of such a set based on an extension of the Lovász theta number to hypergraphs. This bound is at least as good as previously known bounds and for many values of n and t it is better.
We also refine existing spectral methods to show that α(n,t) is at most 2(n+1) for all n and nonpositive t, with equality only at t = −1/n. This allows us to show the uniqueness of the optimal construction at t = −1/n for n at most 5 and to enumerate all possible constructions for n equal to 2 and 3 and nonpositve t.
Keywords
- Programming, Nonlinear
- Continuous Optimization
Status: accepted
Back to the list of papers