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The effectiveness of projection methods for solving systems of linearinequalities is investigated. It is shown that they have a computationaladvantage over some alternatives and that this makes them successful inreal-world applications. This is supported by experimental evidence provided inthis paper on problems of various sizes (up to tens of thousands of unknownssatisfying up to hundreds of thousands of constraints) and by a discussion ofthe demonstrated efficacy of projection methods in numerous scientificpublications and commercial patents (dealing with problems that can have over abillion unknowns and a similar number of constraints).

On the Effectiveness of Projection Methods for Convex Feasibility Problems with Linear Inequality Constraints