  The ancient concept of circumcenter has recently given birth to the
Circumcentered-Reflection method (CRM). CRM was first employed to solve best
approximation problems involving affine subspaces. In this setting, it was
shown to outperform the most prestigious projection based schemes, namely, the
Douglas-Rachford method (DRM) and the method of alternating projections (MAP).
We now prove convergence of CRM for finding a point in the intersection of a
finite number of closed convex sets. This striking result is derived under a
suitable product space reformulation in which a point in the intersection of a
closed convex set with an affine subspace is sought. It turns out that CRM
skillfully tackles the reformulated problem. We also show that for a point in
the affine set the CRM iteration is always closer to the solution set than both
the MAP and DRM iterations. Our theoretical results and numerical experiments,
showing outstanding performance, establish CRM as a powerful tool for solving
general convex feasibility problems.
