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Convergence Analysis of an Inexact Three-Operator Splitting Algorithm.
- Source :
-
Symmetry (20738994) . Nov2018, Vol. 10 Issue 11, p563. 1p. - Publication Year :
- 2018
-
Abstract
- The three-operator splitting algorithm is a new splitting algorithm for finding monotone inclusion problems of the sum of three maximally monotone operators, where one is cocoercive. As the resolvent operator is not available in a closed form in the original three-operator splitting algorithm, in this paper, we introduce an inexact three-operator splitting algorithm to solve this type of monotone inclusion problem. The theoretical convergence properties of the proposed iterative algorithm are studied in general Hilbert spaces under mild conditions on the iterative parameters. As a corollary, we obtain general convergence results of the inexact forward-backward splitting algorithm and the inexact Douglas-Rachford splitting algorithm, which extend the existing results in the literature. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STOCHASTIC convergence
*OPERATOR theory
*PROBLEM solving
*ALGORITHMS
*HILBERT space
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 10
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Symmetry (20738994)
- Publication Type :
- Academic Journal
- Accession number :
- 133220245
- Full Text :
- https://doi.org/10.3390/sym10110563