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Proximal Point Subgradient 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 function on an intersection of two sets in a Hilbert space. One of them is a common fixed point set of a finite family of quasi-nonexpansive mappings while the second one is a common zero point set of finite family of maximal monotone operators. Our goal is to obtain a good approximate solution of the problem in the presence of computational errors. We use the Cimmino proximal point subgradient algorithm, the iterative proximal point subgradient algorithm and the dynamic string-averaging proximal point subgradient algorithm and show that each of them 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. "Proximal Point Subgradient Algorithm," Springer Optimization and Its Applications, in: Optimization on Solution Sets of Common Fixed Point Problems, chapter 0, pages 103-173, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-78849-0_3
    DOI: 10.1007/978-3-030-78849-0_3
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