Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Victor Amarachi Uzor; Timilehin Opeyemi Alakoya; Oluwatosin Temitope Mewomo

doi:10.1515/math-2022-0030

Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Victor Amarachi Uzor, Timilehin Opeyemi Alakoya, Oluwatosin Temitope Mewomo^*

^*Corresponding author for this work

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

51 Citations (Scopus)

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Abstract

In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng's extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.

Original language	English
Pages (from-to)	234-257
Number of pages	24
Journal	Open Mathematics
Volume	20
Issue number	1
DOIs	https://doi.org/10.1515/math-2022-0030
Publication status	Published - 13 Apr 2022
Externally published	Yes

Bibliographical note

Funding Information:
The authors sincerely thank the reviewers for their careful reading, constructive comments, and fruitful suggestions that improved the manuscript. The research of Timilehin Opeyemi Alakoya is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Oluwatosin Temitope Mewomo is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF.

Publisher Copyright:
© 2022 Victor Amarachi Uzor et al., published by De Gruyter.

Keywords

adaptive step size
demicontractive
fixed point
inertial technique
pseudomonotone
strong convergence
Tseng's extragradient method
variational inequalities

ASJC Scopus subject areas

General Mathematics

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10.1515/math-2022-0030Licence: CC BY

Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems
Copyright 2022 the authors. This is an open access article published under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.
Final published version, 2.97 MBLicence: CC BY

Cite this

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title = "Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems",

abstract = "In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng's extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.",

keywords = "adaptive step size, demicontractive, fixed point, inertial technique, pseudomonotone, strong convergence, Tseng's extragradient method, variational inequalities",

author = "Uzor, {Victor Amarachi} and Alakoya, {Timilehin Opeyemi} and Mewomo, {Oluwatosin Temitope}",

note = "Funding Information: The authors sincerely thank the reviewers for their careful reading, constructive comments, and fruitful suggestions that improved the manuscript. The research of Timilehin Opeyemi Alakoya is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Oluwatosin Temitope Mewomo is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF. Publisher Copyright: {\textcopyright} 2022 Victor Amarachi Uzor et al., published by De Gruyter.",

year = "2022",

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doi = "10.1515/math-2022-0030",

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T1 - Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

AU - Uzor, Victor Amarachi

AU - Alakoya, Timilehin Opeyemi

AU - Mewomo, Oluwatosin Temitope

N1 - Funding Information: The authors sincerely thank the reviewers for their careful reading, constructive comments, and fruitful suggestions that improved the manuscript. The research of Timilehin Opeyemi Alakoya is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Oluwatosin Temitope Mewomo is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the NRF. Publisher Copyright: © 2022 Victor Amarachi Uzor et al., published by De Gruyter.

PY - 2022/4/13

Y1 - 2022/4/13

N2 - In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng's extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.

AB - In this paper, we study the problem of finding a common solution of the pseudomonotone variational inequality problem and fixed point problem for demicontractive mappings. We introduce a new inertial iterative scheme that combines Tseng's extragradient method with the viscosity method together with the adaptive step size technique for finding a common solution of the investigated problem. We prove a strong convergence result for our proposed algorithm under mild conditions and without prior knowledge of the Lipschitz constant of the pseudomonotone operator in Hilbert spaces. Finally, we present some numerical experiments to show the efficiency of our method in comparison with some of the existing methods in the literature.

KW - adaptive step size

KW - demicontractive

KW - fixed point

KW - inertial technique

KW - pseudomonotone

KW - strong convergence

KW - Tseng's extragradient method

KW - variational inequalities

U2 - 10.1515/math-2022-0030

DO - 10.1515/math-2022-0030

M3 - Article

AN - SCOPUS:85128854072

SN - 2391-5455

VL - 20

SP - 234

EP - 257

JO - Open Mathematics

JF - Open Mathematics

IS - 1

ER -

Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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