Convergence Results of Forward-Backward Algorithms for Sum of Monotone Operators in Banach Spaces

It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two m...

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Bibliographic Details
Published in:	Resultate der Mathematik Vol. 74; no. 4
Main Author:	Shehu, Yekini
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.12.2019
Subjects:	Mathematics Mathematics and Statistics 65K15 47J20 forward-backward algorithm 90C25 2-uniformly convex Banach space Inclusion problem weak convergence 47H05 47J25 strong convergence
ISSN:	1422-6383, 1420-9012
Online Access:	Get full text
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Summary:	It is well known that many problems in image recovery, signal processing, and machine learning can be modeled as finding zeros of the sum of maximal monotone and Lipschitz continuous monotone operators. Many papers have studied forward-backward splitting methods for finding zeros of the sum of two monotone operators in Hilbert spaces. Most of the proposed splitting methods in the literature have been proposed for the sum of maximal monotone and inverse-strongly monotone operators in Hilbert spaces. In this paper, we consider splitting methods for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators in Banach spaces. We obtain weak and strong convergence results for the zeros of the sum of maximal monotone and Lipschitz continuous monotone operators in Banach spaces. Many already studied problems in the literature can be considered as special cases of this paper.
ISSN:	1422-6383 1420-9012
DOI:	10.1007/s00025-019-1061-4