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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Vydáno v:Resultate der Mathematik Ročník 74; číslo 4
Hlavní autor: Shehu, Yekini
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cham Springer International Publishing 01.12.2019
Témata:
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
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Popis
Shrnutí: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