  In this paper, we consider convex feasibility problems where the underlying
sets are loosely coupled, and we propose several algorithms to solve such
problems in a distributed manner. These algorithms are obtained by applying
proximal splitting methods to convex minimization reformulations of convex
feasibility problems. We also put forth distributed convergence tests which
enable us to establish feasibility or infeasibility of the problem
distributedly, and we provide convergence rate results. Under the assumption
that the problem is feasible and boundedly linearly regular, these convergence
results are given in terms of the distance of the iterates to the feasible set,
which are similar to those of classical projection methods. In case the
feasibility problem is infeasible, we provide convergence rate results that
concern the convergence of certain error-bounds.
