On the linear convergence of the circumcentered-reflection method

Abstract

In order to accelerate the Douglas--Rachford method we recently developed the circumcentered--reflection method, which provides the closest iterate to the solution among all points relying on successive reflections, for the best approximation problem related to two affine subspaces. We now prove that this is still the case when considering a family of finitely many affine subspaces. This property yields linear convergence and incites embedding of circumcenters within classical reflection and projection based methods for more general feasibility problems.

References in corpus (2)

• Circumcentering the Douglas--Rachford method
• The Douglas-Rachford algorithm in the affine-convex case

Cited by in corpus (9)

• On the Circumcentered-Reflection Method for the Convex Feasibility Problem
• The Block-wise Circumcentered-Reflection Method
• The circumcentered-reflection method achieves better rates than alternating projections
• Circumcentering approximate reflections for solving the convex feasibility problem
• On the centralization of the circumcentered-reflection method
• Circumcentric directions of cones
• A successive centralized circumcenter reflection method for the convex feasibility problem
• A finitely convergent circumcenter method for the Convex Feasibility Problem
• Circumcentered methods induced by isometries