  Optimal recovery is a mathematical framework for learning functions from
observational data by adopting a worst-case perspective tied to model
assumptions on the functions to be learned. Working in a finite-dimensional
Hilbert space, we consider model assumptions based on approximability and
observation inaccuracies modeled as additive errors bounded in $\ell_2$. We
focus on the local recovery problem, which amounts to the determination of
Chebyshev centers. Earlier work by Beck and Eldar presented a semidefinite
recipe for the determination of Chebyshev centers. The result was valid in the
complex setting only, but not necessarily in the real setting, since it relied
on the S-procedure with two quadratic constraints, which offers a tight
relaxation only in the complex setting. Our contribution consists in proving
that this semidefinite recipe is exact in the real setting, too, at least in
the particular instance where the quadratic constraints involve orthogonal
projectors. Our argument exploits a previous work of ours, where exact
Chebyshev centers were obtained in a different way. We conclude by stating some
open questions and by commenting on other recent results in optimal recovery.
