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Proximal Point Algorithm

In: Algorithms for Solving Common Fixed Point Problems

Author

Listed:
  • Alexander J. Zaslavski

    (Technion:Israel Institute of Technology)

Abstract

In a Hilbert space, we study the convergence of an iterative proximal point method to a common zero of a finite family of maximal monotone operators under the presence of perturbations. We show that the inexact proximal point method generates an approximate solution if perturbations are summable. We also show that if the perturbations are sufficiently small, then the inexact proximal point method produces approximate solutions.

Suggested Citation

  • Alexander J. Zaslavski, 2018. "Proximal Point Algorithm," Springer Optimization and Its Applications, in: Algorithms for Solving Common Fixed Point Problems, chapter 0, pages 237-253, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-77437-4_6
    DOI: 10.1007/978-3-319-77437-4_6
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