Recently, circumcenter schemes were applied to solving general convex feasibility problems. In order to overcome costly computations of projections and reflections onto convex sets, we present a variant of the circumcentered-reflection method which employs outer-approximate projections, inspired by Fukushima. With a very practical appeal, this notion relies on separating hyperplanes and is considered in our hybrid method for finding a point in the intersection of finitely many convex sets. We derive convergence in general, linear convergence under an error bound condition, and present successful numerical experiments.
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