Some remarks on a successive projection sequence

The successive projection algorithms were introduced by von Neuman [11] and Brègman [3]. These algorithms have a broad applicability in medical imaging, computerized tomography or signal processing. In this paper we focus on a particular projection sequence in which the points are successively projected onto the convex set from which they are the most distant. Among other things, we analyze the convergence of the algorithm and propose a finite termination criterion allowing for the analysis of the complexity of the algorithm. In line with the seminal work by Brègman, an application to linear optimization problems is proposed. This issue illustrates that successive projection algorithms may have some interest for very large finite dimensional problems.