| Article ID: | iaor20122509 |
| Volume: | 51 |
| Issue: | 3 |
| Start Page Number: | 1065 |
| End Page Number: | 1088 |
| Publication Date: | Apr 2012 |
| Journal: | Computational Optimization and Applications |
| Authors: | Censor Yair, Chen Wei, Combettes Patrick, Davidi Ran, Herman Gabor |
| Keywords: | programming: convex |
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).