Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry

2016/09/16 by Machado, Fabrício Caluza, Filho, Fernando Mário de Oliveira · 1 citation
#52C17 #90C22 #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1609.05167

Abstract

The kissing number of ℝⁿ is the maximum number of pairwise-nonoverlapping unit spheres that can simultaneously touch a central unit sphere. Mittelmann and Vallentin (2010), based on the semidefinite programming bound of Bachoc and Vallentin (2008), computed the best known upper bounds for the kissing number for several values of n ≤ 23. In this paper, we exploit the symmetry present in the semidefinite programming bound to provide improved upper bounds for n = 9, …, 23.

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• Conic optimization for extremal geometry

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