  Given a compact subset of a Banach space, the Chebyshev center problem
consists of finding a minimal circumscribing ball containing the set. In this
article we establish a numerically tractable algorithm for solving the
Chebyshev center problem in the context of optimal learning from a finite set
of data points. For a hypothesis space realized as a compact but not
necessarily convex subset of a finite-dimensional subspace of some underlying
Banach space, this algorithm computes the Chebyshev radius and the Chebyshev
center of the hypothesis space, thereby solving the problem of optimal recovery
of functions from data. The algorithm itself is based on, and significantly
extends, recent results for near-optimal solutions of convex semi-infinite
problems by means of targeted sampling, and it is of independent interest.
Several examples of numerical computations of Chebyshev centers are included in
order to illustrate the effectiveness of the algorithm.
