caa a22 4500 463169913 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s10957-007-9163-7 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9163-7 Dudek R. University of Zielona Góra, Zielona Góra, Poland aut Iterative Method for Solving the Linear Feasibility Problem [Elektronische Daten] [R. Dudek] Many optimization problems reduce to the solution of a system of linear inequalities (SLI). Some solution methods use relaxed, averaged projections. Others invoke surrogate constraints (typically stemming from aggregation). This paper proposes a blend of these two approaches. A novelty comes from introducing as surrogate constraint a halfspace defined by differences of algorithmic iterates. The first iteration is identical to surrogate constraints methods. In next iterations, for a given approximation $\bar{x}$ , besides the violated constraints in $\bar{x}$ , we also take into consideration the surrogate inequality, which we have obtained in the previous iteration. The motivation for this research comes from the recent work of Scolnik et al. (Appl. Numer. Math. 41, 499-513, 2002), who studied some projection methods for a system of linear equations. Springer Science+Business Media, LLC, 2007 Linear feasibility problems nationallicence Iterative methods nationallicence Surrogate constraints nationallicence Metric projections nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 401-410 0022-3239 132:3<401 2007 132 10957 https://doi.org/10.1007/s10957-007-9163-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9163-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dudek R. University of Zielona Góra, Zielona Góra, Poland aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/3(2007-03-01), 401-410 0022-3239 132:3<401 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer