Convergence Analysis of an Inexact Three-Operator Splitting Algorithm

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 th...

Full description

Saved in:
Bibliographic Details
Published in:Symmetry (Basel) 2018-11, Vol.10 (11), p.563
Main Authors: Zong, Chunxiang, Tang, Yuchao, Cho, Yeol
Format: Article
Language:English
Subjects:
Algorithms
Convergence
Convex analysis
fixed point
Hilbert space
inexact three-operator splitting algorithm
Iterative algorithms
nonexpansive operator
Optimization
Splitting
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym10110563