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Generalized Krasnoselskii-Mann-type iterations for nonexpansive mappings in Hilbert spaces.
- Source :
- Computational Optimization & Applications; Jul2017, Vol. 67 Issue 3, p595-620, 26p
- Publication Year :
- 2017
-
Abstract
- The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive operators; it is known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a new inexact Krasnoselskii-Mann iteration and prove weak convergence under certain accuracy criteria on the error resulting from the inexactness. We also show strong convergence for a modified inexact Krasnoselskii-Mann iteration under suitable assumptions. The convergence results generalize existing ones from the literature. Applications are given to the Douglas-Rachford splitting method, the Fermat-Weber location problem as well as the alternating projection method by John von Neumann. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09266003
- Volume :
- 67
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Computational Optimization & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 123191378
- Full Text :
- https://doi.org/10.1007/s10589-017-9902-0