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October  2006, 2(4): 451-466. doi: 10.3934/jimo.2006.2.451

Some remarks on a successive projection sequence

Walter Briec 1, and  Bernardin Solonandrasana 1,

1. 

Department of Economics and Management Sciences, University of Perpignan, 52 Avenue Paul Alduy, Perpignan, F-66860, France, France

Received  March 2006 Revised  August 2006 Published  October 2006

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.
Keywords: linear optimization., feasibility problems, successive projections methods, projections onto convex sets.
Mathematics Subject Classification: 49M45, 65J05, 90C2.
Citation: Walter Briec, Bernardin Solonandrasana. Some remarks on a successive projection sequence. Journal of Industrial & Management Optimization, 2006, 2 (4) : 451-466. doi: 10.3934/jimo.2006.2.451
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