  The smallest enclosing circle problem asks for the circle of smallest radius
enclosing a given set of finite points on the plane. This problem was
introduced in the 19th century by Sylvester [17]. After more than a century,
the problem remains very active. This paper is the continuation of our effort
in shedding new light to classical geometry problems using advanced tools of
convex analysis and optimization. We propose and study the following
generalized version of the smallest enclosing circle problem: given a finite
number of nonempty closed convex sets in a reflexive Banach space, find a ball
with the smallest radius that intersects all of the sets.
