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On the Effectiveness of Projection Methods for Convex Feasibility

Yair Censor(yair***at***math.haifa.ac.il)
Wei Chen(wchen***at***gc.cuny.edu)
Patrick L. Combettes(plc***at***math.jussieu.fr)
Ran Davidi(r_davidi***at***yahoo.com)
Gabor T. Herman(gabortherman***at***yahoo.com)

Abstract: The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in 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).

Keywords: Projection methods · Convex feasibility problems · Numerical evaluation· Optimization · Linear inequalities · Sparse matrices

Category 1: Applications -- Science and Engineering

Category 2: Linear, Cone and Semidefinite Programming

Category 3: Applications -- Science and Engineering (Biomedical Applications )

Citation: Technical Report, Submitted for Publication.

Download: [PDF]

Entry Submitted: 12/22/2009
Entry Accepted: 12/22/2009
Entry Last Modified: 12/22/2009

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