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Convex Feasibility Problems

In: Approximate Solutions of Common Fixed-Point Problems

Author

Listed:
  • Alexander J. Zaslavski

    (The Technion - Israel Institute of Technology)

Abstract

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

  • Alexander J. Zaslavski, 2016. "Convex Feasibility Problems," Springer Optimization and Its Applications, in: Approximate Solutions of Common Fixed-Point Problems, chapter 0, pages 341-384, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-33255-0_10
    DOI: 10.1007/978-3-319-33255-0_10
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