论文标题
确定性算法，用于计算有限正跨度集合的余弦度量
A deterministic algorithm to compute the cosine measure of a finite positive spanning set
论文作者
论文摘要
最初于1954年开发的正面基础和正跨度集合在无衍生化优化（DFO）中是一个有价值的概念。可以通过{\ em余弦度量}来量化积极基础（或正跨度集合）的质量，并且某些DFO算法的收敛性能与该度量的值密切相关。但是，目前尚不清楚如何从定义中以积极的基础计算余弦度量。在本文中，提供了一种确定性算法，以计算任何积极基础或有限的阳性跨度集的余弦度量。事实证明，该算法可以在有限的时间内返回余弦度量的确切值。
Originally developed in 1954, positive bases and positive spanning sets have been found to be a valuable concept in derivative-free optimization (DFO). The quality of a positive basis (or positive spanning set) can be quantified via the {\em cosine measure} and convergence properties of certain DFO algorithms are intimately linked to the value of this measure. However, it is unclear how to compute the cosine measure for a positive basis from the definition. In this paper, a deterministic algorithm to compute the cosine measure of any positive basis or finite positive spanning set is provided. The algorithm is proven to return the exact value of the cosine measure in finite time.
