Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems

A. J. Zaslavski ()
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A. J. Zaslavski: Technion

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 3, No 12, 803-819

Abstract: 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.

Keywords: Approximate solution; Feasibility problem; Hilbert space; Subgradient projection algorithm (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10957-012-0238-8

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