Circumcentering outer-approximate projections and reflections for the convex feasibility problem

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.

Texto informado pelo autor.