Faculties of Mathematics Computer Sciences and Econometrics

Many optimization problems reduce to the solution of a system of lin-ear inequalities (SLI). Some solution methods use relaxed, averaged projections. Others invoke surrogate constraints (typically stemming from aggregation). This paper proposed a blend of these two ap-proaches. A novelty comes with introducing as surrogate constrained a halfspace defined by differences of algorithmic iterates. The first iteration is identical to surrogate constraints methods. In next itera-tions, for a given approximation x̄, besides the violated constraints in x̄, we also take into consideration the surrogate inequality, which we have obtained in the previous iteration. The motivation for this research comes from the work of H. Scolnik et al. [1], who studied some projection methods for a system of linear equations.