  The problem of finding a best approximation pair of two sets, which in turn
generalizes the well known convex feasibility problem, has a long history that
dates back to work by Cheney and Goldstein in 1959.
  In 2018, Aharoni, Censor, and Jiang revisited this problem and proposed an
algorithm that can be used when the two sets are finite intersections of
halfspaces. Motivated by their work, we present alternative algorithms that
utilize projection and proximity operators. Numerical experiments indicate that
these methods are competitive and sometimes superior to the one proposed by
Aharoni et al.
