Iterative method with inertial terms for nonexpansive mappings: applications to compressed sensing

Our interest in this paper is to introduce a Halpern-type algorithm with both inertial terms and errors for approximating fixed point of a nonexpansive mapping. We obtain strong convergence of the sequence generated by our proposed method in real Hilbert spaces under some reasonable assumptions on t...

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Bibliographic Details
Published in:Numerical algorithms Vol. 83; no. 4; pp. 1321 - 1347
Main Authors: Shehu, Yekini, Iyiola, Olaniyi S., Ogbuisi, Ferdinard U.
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2020
Springer Nature B.V
Subjects:
Algebra
Algorithms
Codes
Computer Science
Convergence
Hilbert space
Inverse problems
Iterative methods
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Theory of Computation
Halpern-type algorithm
Strong convergence
65K15
47J20
90C25
Hilbert spaces
Inertial terms
47H05
47J25
Nonexpansive mappings
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:Our interest in this paper is to introduce a Halpern-type algorithm with both inertial terms and errors for approximating fixed point of a nonexpansive mapping. We obtain strong convergence of the sequence generated by our proposed method in real Hilbert spaces under some reasonable assumptions on the sequence of parameters. As applications, we present some strong convergence results for monotone inclusion, variational inequality problem, linear inverse problem, and LASSO problem in Compressed Sensing. Our result improves the rate of convergence of existing Halpern method for monotone inclusion, variational inequality problem, linear inverse problem and LASSO problem in compressed sensing as illustrated in our numerical examples both in finite and infinite dimensional Hilbert spaces.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00727-5