AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

Jamilu Abubakar; Poom Kumam; Abor Isa Garba; Muhammad Sirajo Abdullahi; Abdulkarim Hassan Ibrahim; Wachirapong Jirakitpuwapat

doi:10.3934/jimo.2021160

AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

Jamilu Abubakar, Poom Kumam^*, Abor Isa Garba, Muhammad Sirajo Abdullahi, Abdulkarim Hassan Ibrahim, Wachirapong Jirakitpuwapat

^*Corresponding author for this work

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

7 Scopus citations

Abstract

A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.

Original language	English
Pages (from-to)	4311-4331
Number of pages	21
Journal	Journal of Industrial and Management Optimization
Volume	18
Issue number	6
DOIs	https://doi.org/10.3934/jimo.2021160
State	Published - Nov 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022, Journal of Industrial and Management Optimization. All rights reserved.

Keywords

Image debluring
Inertial step
Maximal monotone operator
Nash equilibrium
Split convex feasibility method
Split variational inclusion problem

ASJC Scopus subject areas

Business and International Management
Strategy and Management
Control and Optimization
Applied Mathematics

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10.3934/jimo.2021160

Cite this

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title = "AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS",

abstract = "A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.",

keywords = "Image debluring, Inertial step, Maximal monotone operator, Nash equilibrium, Split convex feasibility method, Split variational inclusion problem",

author = "Jamilu Abubakar and Poom Kumam and Garba, \{Abor Isa\} and Abdullahi, \{Muhammad Sirajo\} and Ibrahim, \{Abdulkarim Hassan\} and Wachirapong Jirakitpuwapat",

year = "2022",

month = nov,

doi = "10.3934/jimo.2021160",

language = "English",

volume = "18",

pages = "4311--4331",

journal = "Journal of Industrial and Management Optimization",

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T1 - AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

AU - Abubakar, Jamilu

AU - Kumam, Poom

AU - Garba, Abor Isa

AU - Abdullahi, Muhammad Sirajo

AU - Ibrahim, Abdulkarim Hassan

AU - Jirakitpuwapat, Wachirapong

PY - 2022/11

Y1 - 2022/11

N2 - A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.

AB - A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.

KW - Image debluring

KW - Inertial step

KW - Maximal monotone operator

KW - Nash equilibrium

KW - Split convex feasibility method

KW - Split variational inclusion problem

UR - https://www.scopus.com/pages/publications/85137617693

U2 - 10.3934/jimo.2021160

DO - 10.3934/jimo.2021160

M3 - Article

AN - SCOPUS:85137617693

SN - 1547-5816

VL - 18

SP - 4311

EP - 4331

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 6

ER -

AN EFFICIENT ITERATIVE METHOD FOR SOLVING SPLIT VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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