Abstract
In the present paper, we use subgradient projection algorithms for solving convex feasibility problems. We show that almost all iterates, generated by a subgradient projection algorithm in a Hilbert space, are approximate solutions. Moreover, we obtain an estimate of the number of iterates which are not approximate solutions. In a finite-dimensional case, we study the behavior of the subgradient projection algorithm in the presence of computational errors. Provided computational errors are bounded, we prove that our subgradient projection algorithm generates a good approximate solution after a certain number of iterates.
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The author thanks the referees for useful remarks.
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Communicated by Michael Patriksson.
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Zaslavski, A.J. Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems. J Optim Theory Appl 157, 803–819 (2013). https://doi.org/10.1007/s10957-012-0238-8
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DOI: https://doi.org/10.1007/s10957-012-0238-8