In this paper, the cone of completely-positive functions, a subset of the cone of positive-type functions, is introduced. This cone is then used 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.

中文翻译：

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完整的积极性和避免距离集

本文介绍了正函数锥的一个子集——完全正函数锥。然后使用该锥体将最大密度避免距离集完全表征为凸优化问题的最优解。作为这种表征的结果，可以证明和改进关于球体和欧几里得空间中的距离避免集的许多结果。