Complete positivity and distance-avoiding sets

Evan DeCorte, Fernando Mário de Oliveira Filho, Frank Vallentin

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Abstract

We introduce the cone of completely positive functions, a subset of the cone of positive-type functions, and use it to fully characterize maximum-density distance-avoiding sets as the optimal solutions of a convex optimization problem. As a consequence of this characterization, it is possible to reprove and improve many results concerning distance-avoiding sets on the sphere and in Euclidean space.

Original languageEnglish
Number of pages72
JournalMathematical Programming
DOIs
Publication statusPublished - 2020

Keywords

  • Chromatic number of Euclidean space
  • Copositive programming
  • Hadwiger-Nelson problem
  • Harmonic analysis
  • Semidefinite programming

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