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Extrapolation algorithm for affine-convex feasibility problems. (English) Zbl 1098.65060

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.

65K05Mathematical programming (numerical methods)
90C25Convex programming
47J25Iterative procedures (nonlinear operator equations)
47N10Applications of operator theory in optimization, convex analysis, programming, economics
90C48Programming in abstract spaces
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