Convergence of string-averaging projection schemes for inconsistent convex feasibility problems

Yair Censor (yairmath.haifa.ac.il)
Eli Tom (eli.tomintel.com)

Abstract: 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 (BIP) 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; convex feasibility; string-averaging; product space; inconsistent feasibility problem

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: Optimization Methods and Software, Vol. 18 (2003), pp. 543-554.

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Entry Submitted: 08/04/2003
Entry Accepted: 08/04/2003
Entry Last Modified: 10/06/2003

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