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Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems

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  • A. J. Zaslavski

    (Technion)

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.

Suggested Citation

  • A. J. Zaslavski, 2013. "Subgradient Projection Algorithms and Approximate Solutions of Convex Feasibility Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 803-819, June.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:3:d:10.1007_s10957-012-0238-8
    DOI: 10.1007/s10957-012-0238-8
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