Speaker.  Yunier Bello Cruz, Northern Illinois University

Title.  On the Circumcentered-Reflection Method

Abstract. In this talk, we will introduce the Centralized Circumcentered-Reflection Method (cCRM), a novel iteration scheme designed to identify a point at the intersection of two closed convex sets without resorting to a product space reformulation. Unlike its predecessor, the Circumcentered-Reflection Method (CRM), the cCRM ensures convergence in general convex sets, showing both linear and superlinear convergence under certain conditions. Through a comparative analysis with the Method of Alternating Projections (MAP), we will demonstrate the superior performance of CRM and cCRM, backed by promising numerical experiments and theoretical proofs.