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Zbl 1098.65060
Bauschke, Heinz H.; Combettes, Patrick L.; Kruk, Serge G.
Extrapolation algorithm for affine-convex feasibility problems. (English)
[J] Numer. Algorithms 41, No. 3, 239-274 (2006). ISSN 1017-1398; ISSN 1572-9265/e

The problem is to find a common point of a countable family of closed affine subspaces and convex sets in a Hilbert space. A general algorithmic framework is proposed, which unifies the existing convergence results for a wide range of projection, subgradient projection, proximal, and fixed-point methods. A new extrapolation algorithm based on the general framework is presented, its convergence is established, and connections with existing results are shown. In the concluding section of the paper, the proposed algorithm is specialized to the case of finding a common point of two sets only, namely of a closed affine subspace and a closed convex subset of a Hilbert space. Numerical simulation results confirming the expected acceleration in this special case are presented.
[Karel Zimmermann (Praha)]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C25 Convex programming
47J25 Methods for solving nonlinear operator equations (general)
47N10 Appl. of operator theory in optimization, math. programming, etc.
90C48 Programming in abstract spaces

Keywords: affinite sets; convex feasibility problem; convex sets; extrapolation; Hilbert space; projection method; convergence; numerical results

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