Primal and dual algorithms for the minimum covering Euclidean ball of a set of Euclidean balls in ${\mathbb{R}}^n$

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.