Solving Nonconvex Feasibility Problem on a Sphere and a Closed Ball by Douglas–Rachford Algorithm

Abstract

In recent times, a variety of nonconvex feasibility problems have been solved empirically by employing Douglas–Rachford (DR) splitting methods. However, this theory is not adequate in explaining the observed success and is more concerned with the local convergence. In this paper, we study the convergence of the DR splitting method for finding a point of intersection of a closed ball and a sphere in the [Formula: see text]-dimensional Euclidean spaces. Also, we provide the region for the global convergence of the DR splitting method.