New self-adaptive step size algorithms for solving split variational inclusion problems and its applications

In this paper, we study a special instance of the split inverse problem (SIP), which is the split variational inclusion problem (SVIP). Three simple iterative methods for solving it are introduced and weak and strong convergence theorems are established under mild and standard assumptions. As an app...

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Bibliographic Details
Published in:Numerical algorithms Vol. 83; no. 1; pp. 305 - 331
Main Authors: Tang, Yan, Gibali, Aviv
Format: Journal Article
Language:English
Published: New York Springer US 01.01.2020
Springer Nature B.V
Subjects:
Adaptive algorithms
Algebra
Algorithms
Computer Science
Continuity (mathematics)
Data compression
Feasibility
Inverse problems
Iterative methods
Mathematical analysis
Mathematics
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Self-adaptive
Strong convergence
Split variational inclusion problem
Convex minimization problems
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, we study a special instance of the split inverse problem (SIP), which is the split variational inclusion problem (SVIP). Three simple iterative methods for solving it are introduced and weak and strong convergence theorems are established under mild and standard assumptions. As an application, the problem of minimizing two proper, convex, and lower semi-continuous functions is considered. We compare and illustrate the efficiency and applicability of our schemes for several numerical experiments as well as an example in the field of compressed sensing.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-019-00683-0