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The circumcentered-reflection method (CRM) has been applied for solvingconvex feasibility problems. CRM iterates by computing a circumcenter upon acomposition of reflections with respect to convex sets. Since reflections arebased on exact projections, their computation might be costly. In this regard,we introduce the circumcentered approximate-reflection method (CARM), whosereflections rely on outer-approximate projections. The appeal of CARM is that,in rather general situations, the approximate projections we employ areavailable under low computational cost. We derive convergence of CARM andlinear convergence under an error bound condition. We also present successfultheoretical and numerical comparisons of CARM to the original CRM, to theclassical method of alternating projections (MAP) and to a correspondentouter-approximate version of MAP, referred to as MAAP. Along with our resultsand numerical experiments, we present a couple of illustrative examples.

Circumcentering approximate reflections for solving the convex feasibility problem