Complete positivity and distance-avoiding sets
Metric Geometry
2023-09-14 v4 Functional Analysis
Optimization and Control
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.
Keywords
Cite
@article{arxiv.1804.09099,
title = {Complete positivity and distance-avoiding sets},
author = {Evan DeCorte and Fernando Mário de Oliveira Filho and Frank Vallentin},
journal= {arXiv preprint arXiv:1804.09099},
year = {2023}
}
Comments
57 pages; final version published at Math. Program