Iterative Method for Solving the Linear Feasibility Problem

R. Dudek ()
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R. Dudek: University of Zielona Góra

Journal of Optimization Theory and Applications, 2007, vol. 132, issue 3, No 3, 410 pages

Abstract: Abstract 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.

Keywords: Linear feasibility problems; Iterative methods; Surrogate constraints; Metric projections (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9163-7

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