New iterative methods for linear inequalities

New iterative methods for solving systems of linear inequalities are presented. Each step in these methods consists of finding the orthogonal projection of the current point onto a hyperplane corresponding to a surrogate constraint which is constructed through a positive combination of a group of violated constraints. Both sequential and parallel implementations are discussed.The authors are grateful to a referee for pointing out the result in Lemma 5.1 and its importance in the proof of Theorem 5.1. This work was supported partially by NSF Grant No. ECS-85-21183.