Iterative methods for solving proximal split minimization problems

In this paper, we propose two iterative algorithms for finding the minimum-norm solution of a split minimization problem. We prove strong convergence of the sequences generated by the proposed algorithms. The iterative schemes are proposed in such a way that the selection of the step-sizes does not...

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Bibliographic Details
Published in:Numerical algorithms 2018-05, Vol.78 (1), p.193-215
Main Authors: Abbas, M., AlShahrani, M., Ansari, Q. H., Iyiola, O. S., Shehu, Y.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Hilbert space
Iterative algorithms
Iterative methods
Mathematics
Numeric Computing
Numerical Analysis
Optimization
Original Paper
Theory of Computation
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Summary:In this paper, we propose two iterative algorithms for finding the minimum-norm solution of a split minimization problem. We prove strong convergence of the sequences generated by the proposed algorithms. The iterative schemes are proposed in such a way that the selection of the step-sizes does not need any prior information about the operator norm. We further give some examples to numerically verify the efficiency and implementation of our new methods and compare the two algorithms presented. Our results act as supplements to several recent important results in this area.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-017-0372-3