Circumcentering approximate reflections for solving the convex feasibility problem

Abstract The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon composition of reflections with respect to sets. Since are based on exact projections, their computation might be costly. In this regard, we introduce the circumcentered approximate-reflection (CARM), whose rely outer-approximate projections. appeal CARM is that, in rather general situations, approximate projections employ available under low computational cost. We derive convergence and linear an error bound condition. also present successful theoretical numerical comparisons original CRM, classical alternating (MAP), correspondent version MAP, referred as MAAP. Along our results experiments, couple illustrative examples.