2

On the Circumcentered-Reflection Method for the Convex Feasibility Problem

The ancient concept of circumcenter has recently given birth to the Circumcentered-Reflection method (CRM). CRM was firstly employed to solve best approximation problems involving affine subspaces. In this setting, it was shown to outperform the most …

The Block-Wise Circumcentered– Reflection Method

The elementary Euclidean concept of circumcenter has recently been employed to improve two aspects of the classical Douglas– Rachford method for projecting onto the intersection of affine subspaces....

Circumcentering the Douglas–Rachford Method

We introduce and study a geometric modification of the Douglas– Rachford method called the Circumcentered– Douglas– Rachford method. This method iterates by taking the intersection of bisectors of reflection steps for solving certain classes of …

On the Linear Convergence of the Circumcentered-Reflection Method

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 …