An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

Kanikar Muangchoo; Abubakar Adamu; Abdulkarim Hassan Ibrahim; Auwal Bala Abubakar

doi:10.1007/s40314-022-02064-1

An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

Kanikar Muangchoo^*
, Abubakar Adamu
, Abdulkarim Hassan Ibrahim
, Auwal Bala Abubakar

^*Corresponding author for this work

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

15 Scopus citations

Abstract

In this work, an inertial Halpern-type algorithm involving monotone operators is proposed in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the iterates generated by the algorithm is proved to a zero of sum of two monotone operators. Furthermore, an application of the method to image recovery problems is presented. In addition, a numerical example on the classical Banach space l32(R) is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature.

Original language	English
Article number	364
Journal	Computational and Applied Mathematics
Volume	41
Issue number	8
DOIs	https://doi.org/10.1007/s40314-022-02064-1
State	Published - Dec 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

Keywords

Convex minimization
Image recovery
Monotone
Zeros

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s40314-022-02064-1

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title = "An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems",

abstract = "In this work, an inertial Halpern-type algorithm involving monotone operators is proposed in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the iterates generated by the algorithm is proved to a zero of sum of two monotone operators. Furthermore, an application of the method to image recovery problems is presented. In addition, a numerical example on the classical Banach space l32(R) is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature.",

keywords = "Convex minimization, Image recovery, Monotone, Zeros",

author = "Kanikar Muangchoo and Abubakar Adamu and Ibrahim, \{Abdulkarim Hassan\} and Abubakar, \{Auwal Bala\}",

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doi = "10.1007/s40314-022-02064-1",

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AU - Muangchoo, Kanikar

AU - Adamu, Abubakar

AU - Ibrahim, Abdulkarim Hassan

AU - Abubakar, Auwal Bala

PY - 2022/12

Y1 - 2022/12

N2 - In this work, an inertial Halpern-type algorithm involving monotone operators is proposed in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the iterates generated by the algorithm is proved to a zero of sum of two monotone operators. Furthermore, an application of the method to image recovery problems is presented. In addition, a numerical example on the classical Banach space l32(R) is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature.

AB - In this work, an inertial Halpern-type algorithm involving monotone operators is proposed in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the iterates generated by the algorithm is proved to a zero of sum of two monotone operators. Furthermore, an application of the method to image recovery problems is presented. In addition, a numerical example on the classical Banach space l32(R) is presented to support the main theorem. Finally, the performance of the proposed algorithm is compared with that of some existing algorithms in the literature.

KW - Convex minimization

KW - Image recovery

KW - Monotone

KW - Zeros

UR - https://www.scopus.com/pages/publications/85140600563

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DO - 10.1007/s40314-022-02064-1

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JO - Computational and Applied Mathematics

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IS - 8

M1 - 364

ER -

An inertial Halpern-type algorithm involving monotone operators on real Banach spaces with application to image recovery problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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