Complete positivity and distance-avoiding sets

• 成果类型: Article
• 署名作者: DeCorte, Evan; Filho, Fernando Mario de Oliveira; Vallentin, Frank
• 署名单位: McGill University; Delft University of Technology; University of Cologne
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-020-01562-6
• 发表日期: 2022
• 页码: 487-558
• 关键词: sphere packing problem; density; THEOREM; realization

摘要

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.