Circumcentering approximate reflections for fixing the convex feasibility downside
Authors: Guilherme Araújo, Reza Arefidamghani, Roger Behling, Yunier Bello-Cruz, Alfredo Iusem, Luiz-Rafael Santos
Summary: The circumcentered-reflection technique (CRM) has been utilized for fixing convex feasibility issues. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex units. Since reflections are primarily based on precise projections, their computation may be expensive. On this regard, we introduce the circumcentered approximate-reflection technique (CARM), whose reflections depend on outer-approximate projections. The enchantment of CARM is that, in relatively normal conditions, the approximate projections we make use of can be found underneath low computational value. We derive convergence of CARM and linear convergence underneath an error certain situation. We additionally current profitable theoretical and numerical comparisons of CARM to the unique CRM, to the classical technique of alternating projections (MAP) and to a correspondent outer-approximate model of MAP, known as MAAP. Together with our outcomes and numerical experiments, we current a few illustrative examples
