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Fixed Point Gradient Projection Algorithm

In: Optimization on Solution Sets of Common Fixed Point Problems

Author

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  • Alexander J. Zaslavski

    (Technion - Israel Institute of Technology)

Abstract

In this chapter we consider a minimization of a convex smooth function on a solution set of a convex feasibility problem in a general Hilbert space using the fixed point gradient projection algorithm. Our goal is to obtain a good approximate solution of the problem in the presence of computational errors. We show that an algorithm generates a good approximate solution, if the sequence of computational errors is bounded from above by a small constant. Moreover, if we known computational errors for our algorithm, we find out what an approximate solution can be obtained and how many iterates one needs for this.

Suggested Citation

  • Alexander J. Zaslavski, 2021. "Fixed Point Gradient Projection Algorithm," Springer Optimization and Its Applications, in: Optimization on Solution Sets of Common Fixed Point Problems, chapter 0, pages 265-288, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-78849-0_7
    DOI: 10.1007/978-3-030-78849-0_7
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