No abstract

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 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 IR 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.