  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.
