  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).
