Convergence of string-averaging projection schemes for inconsistent convex feasibility problems. (English) Zbl 1065.65074
Summary: We study iterative projection algorithms for the convex feasibility problem of finding a point in the intersection of finitely many nonempty, closed and convex subsets in the Euclidean space. We propose (without proof) an algorithmic scheme which generalizes both the string-averaging algorithm and the block-iterative projections method with fixed blocks and prove convergence of the string-averaging method in the inconsistent case by translating it into a fully sequential algorithm in the product space.
Keywords:
projection methods; product space; inconsistent feasibility problem; string-averaging algorithm; convergence; algorithmReferences:
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