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.
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Zaslavski AJ (2016) Approximate solutions of common fixed point problems. Springer optimization and its applications. Springer, New York
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Zaslavski, A.J. (2018). Proximal Point Algorithm. In: Algorithms for Solving Common Fixed Point Problems. Springer Optimization and Its Applications, vol 132. Springer, Cham. https://doi.org/10.1007/978-3-319-77437-4_6
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DOI: https://doi.org/10.1007/978-3-319-77437-4_6
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