A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

Timilehin Opeyemi Alakoya; Lateef Olakunle Jolaoso; Oluwatosin Temitope Mewomoİ

doi:10.3934/jimo.2020152

A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

Timilehin Opeyemi Alakoya, Lateef Olakunle Jolaoso, Oluwatosin Temitope Mewomoİ^*

^*Corresponding author for this work

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

26 Citations (Scopus)

Abstract

We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.

Original language	English
Pages (from-to)	239-265
Number of pages	27
Journal	Journal of Industrial and Management Optimization
Volume	18
Issue number	1
Early online date	01 Oct 2020
DOIs	https://doi.org/10.3934/jimo.2020152
Publication status	Published - Jan 2022
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments. The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and

Publisher Copyright:
© 2022. All Rights Reserved.

Keywords

inertia
k-demicontractive mappings
quasi-nonexpansive mappings
Split variational inclusion problems
strong convergence

ASJC Scopus subject areas

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

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10.3934/jimo.2020152Licence: Unspecified

Cite this

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title = "A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications",

abstract = "We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.",

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author = "Alakoya, {Timilehin Opeyemi} and Jolaoso, {Lateef Olakunle} and Mewomoİ, {Oluwatosin Temitope}",

note = "Funding Information: Acknowledgments. The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and Publisher Copyright: {\textcopyright} 2022. All Rights Reserved.",

year = "2022",

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doi = "10.3934/jimo.2020152",

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AU - Alakoya, Timilehin Opeyemi

AU - Jolaoso, Lateef Olakunle

AU - Mewomoİ, Oluwatosin Temitope

N1 - Funding Information: Acknowledgments. The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and Publisher Copyright: © 2022. All Rights Reserved.

PY - 2022/1

Y1 - 2022/1

N2 - We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.

AB - We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.

KW - inertia

KW - k-demicontractive mappings

KW - quasi-nonexpansive mappings

KW - Split variational inclusion problems

KW - strong convergence

U2 - 10.3934/jimo.2020152

DO - 10.3934/jimo.2020152

M3 - Article

AN - SCOPUS:85123457871

SN - 1547-5816

VL - 18

SP - 239

EP - 265

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 1

ER -

A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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