On the effectiveness of projection methods for convex feasibility problems with linear inequality constraints

  • Authors:

  • Yair Censor;Wei Chen;Patrick L. Combettes;Ran Davidi;Gabor T. Herman

  • Affiliations:

  • Department of Mathematics, University of Haifa, Haifa, Israel 31905;Department of Computer Science, The Graduate Center, City University of New York, New York, USA 10016;Laboratoire Jacques-Louis Lions --- UMR CNRS 7598, UPMC Université Paris 06, Paris, France 75005;Department of Computer Science, The Graduate Center, City University of New York, New York, USA 10016;Department of Computer Science, The Graduate Center, City University of New York, New York, USA 10016

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2012

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Abstract

The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they often have a computational advantage over alternatives that have been proposed for solving the same problem and that this makes them successful in many real-world applications. This is supported by experimental evidence provided in this paper on problems of various sizes (up to tens of thousands of unknowns satisfying up to hundreds of thousands of constraints) and by a discussion of the demonstrated efficacy of projection methods in numerous scientific publications and commercial patents (dealing with problems that can have over a billion unknowns and a similar number of constraints).