论文标题
最小覆盖欧几里得球的原始算法和双重算法，一组欧几里得球，$ \ mathbb {r}^n $
Primal and dual algorithms for the minimum covering Euclidean ball of a set of Euclidean balls in $\mathbb{R}^n$
论文作者
论文摘要
开发了原始算法和双重算法，用于解决$ n $维凸优化的问题，即在欧几里得球上找到覆盖$ m $的欧几里得球的欧几里得球，每个球都带有给定的中心和半径。每种算法都是基于一个定向搜索方法，在该方法中，搜索路径可以是$ \ Mathbb {r}^n $中的射线或二维圆锥部分。在每次迭代中，搜索路径都是由双对点的相交构建的，其中双分组是超平面或$ n $维的倍boloid骨。明确确定沿每个搜索路径的最佳步长。
Primal and dual algorithms are developed for solving the $n$-dimensional convex optimization problem of finding the Euclidean ball of minimum radius that covers $m$ given Euclidean balls, each with a given center and radius. Each algorithm is based on a directional search method in which a search path may be a ray or a two-dimensional conic section in $\mathbb{R}^n$. At each iteration, a search path is constructed by the intersection of bisectors of pairs of points, where the bisectors are either hyperplanes or $n$-dimensional hyperboloids. The optimal step size along each search path is determined explicitly.
