Iterative methods for solving proximal split minimization problems

M. Abbas; M. AlShahrani; Q. H. Ansari; O. S. Iyiola; Y. Shehu

doi:10.1007/s11075-017-0372-3

Iterative methods for solving proximal split minimization problems

M. Abbas, M. AlShahrani, Q. H. Ansari^*, O. S. Iyiola, Y. Shehu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

42 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	193-215
Number of pages	23
Journal	Numerical Algorithms
Volume	78
Issue number	1
DOIs	https://doi.org/10.1007/s11075-017-0372-3
State	Published - 1 May 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.

Keywords

Iterative methods
Moreau-Yosida approximate
Prox-regularity
Proximal split minimization problems
Strong convergence

ASJC Scopus subject areas

Applied Mathematics

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10.1007/s11075-017-0372-3

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title = "Iterative methods for solving proximal split minimization problems",

abstract = "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.",

keywords = "Iterative methods, Moreau-Yosida approximate, Prox-regularity, Proximal split minimization problems, Strong convergence",

author = "M. Abbas and M. AlShahrani and Ansari, \{Q. H.\} and Iyiola, \{O. S.\} and Y. Shehu",

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year = "2018",

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T1 - Iterative methods for solving proximal split minimization problems

AU - Abbas, M.

AU - AlShahrani, M.

AU - Ansari, Q. H.

AU - Iyiola, O. S.

AU - Shehu, Y.

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Iterative methods

KW - Moreau-Yosida approximate

KW - Prox-regularity

KW - Proximal split minimization problems

KW - Strong convergence

UR - https://www.scopus.com/pages/publications/85025098239

U2 - 10.1007/s11075-017-0372-3

DO - 10.1007/s11075-017-0372-3

M3 - Article

AN - SCOPUS:85025098239

SN - 1017-1398

VL - 78

SP - 193

EP - 215

JO - Numerical Algorithms

JF - Numerical Algorithms

IS - 1

ER -

Iterative methods for solving proximal split minimization problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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