Convergence Rate Analysis of Inertial Krasnoselskii-Mann Type Iteration with Applications

It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii-Mann it...

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Vydáno v:Numerical functional analysis and optimization Ročník 39; číslo 10; s. 1077 - 1091
Hlavní autor: Shehu, Yekini
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 27.07.2018
Taylor & Francis Ltd
Témata:
Convergence
Convergence rate
Hilbert space
Hilbert spaces
inertial terms
Iterative methods
nonexpansive mapping
Operators (mathematics)
ISSN:0163-0563, 1532-2467
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Shrnutí:It is well known that the Krasnoselskii-Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii-Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas-Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii-Mann iteration in the literature.
Bibliografie:ObjectType-Article-1
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2018.1477799