Complete positivity and distance-avoiding sets

Evan DeCorte, Fernando Mário de Oliveira Filho*, Frank Vallentin

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
19 Downloads (Pure)


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
Publication statusPublished - 2020


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


Dive into the research topics of 'Complete positivity and distance-avoiding sets'. Together they form a unique fingerprint.

Cite this