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