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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.