An inertial iterative algorithm for approximating common solutions to split equalities of some nonlinear optimization problems

O. T. Mewomo; G. N. Ogwo; T. O. Alakoya

doi:10.1007/s40306-023-00521-5

An inertial iterative algorithm for approximating common solutions to split equalities of some nonlinear optimization problems

O. T. Mewomo^*, G. N. Ogwo, T. O. Alakoya

^*Corresponding author for this work

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Abstract

In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.

Original language	English
Pages (from-to)	621-650
Number of pages	30
Journal	Acta Mathematica Vietnamica
Volume	48
Issue number	4
DOIs	https://doi.org/10.1007/s40306-023-00521-5
Publication status	Published - 01 Dec 2023
Externally published	Yes

Bibliographical note

Funding Information:
The authors thank the reviewers for the time spent and efforts made to read through the manuscript and for their constructive comments and recommendations, which have helped to improve on the quality of the article. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author acknowledges with thanks the scholarship and financial support from the University of KwaZulu-Natal (UKZN) Doctoral Scholarship. The research of the third author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF.

Funding Information:
Open access funding provided by University of KwaZulu-Natal. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author is funded by University of KwaZulu-Natal, Durban, South Africa Doctoral Fellowship. The third author is funded by University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship.

Publisher Copyright:
© 2024, The Author(s).

Keywords

Equilibrium problem
Inertial technique
Nonexpansive semigroup
Self-adaptive step size
Split equality problems
Variational inequalities

ASJC Scopus subject areas

General Mathematics

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10.1007/s40306-023-00521-5Licence: CC BY

An inertial iterative algorithm for approximating common solutions to split equalities of some nonlinear optimization problems
Copyright 2023 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, 982 KBLicence: CC BY

Cite this

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title = "An inertial iterative algorithm for approximating common solutions to split equalities of some nonlinear optimization problems",

abstract = "In this paper, we introduce a new inertial Tseng{\textquoteright}s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.",

keywords = "Equilibrium problem, Inertial technique, Nonexpansive semigroup, Self-adaptive step size, Split equality problems, Variational inequalities",

author = "Mewomo, {O. T.} and Ogwo, {G. N.} and Alakoya, {T. O.}",

note = "Funding Information: The authors thank the reviewers for the time spent and efforts made to read through the manuscript and for their constructive comments and recommendations, which have helped to improve on the quality of the article. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author acknowledges with thanks the scholarship and financial support from the University of KwaZulu-Natal (UKZN) Doctoral Scholarship. The research of the third author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF. Funding Information: Open access funding provided by University of KwaZulu-Natal. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author is funded by University of KwaZulu-Natal, Durban, South Africa Doctoral Fellowship. The third author is funded by University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. Publisher Copyright: {\textcopyright} 2024, The Author(s).",

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AU - Ogwo, G. N.

AU - Alakoya, T. O.

N1 - Funding Information: The authors thank the reviewers for the time spent and efforts made to read through the manuscript and for their constructive comments and recommendations, which have helped to improve on the quality of the article. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author acknowledges with thanks the scholarship and financial support from the University of KwaZulu-Natal (UKZN) Doctoral Scholarship. The research of the third author is wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF. Funding Information: Open access funding provided by University of KwaZulu-Natal. The first author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The second author is funded by University of KwaZulu-Natal, Durban, South Africa Doctoral Fellowship. The third author is funded by University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. Publisher Copyright: © 2024, The Author(s).

PY - 2023/12/1

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N2 - In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.

AB - In this paper, we introduce a new inertial Tseng’s extragradient method with self-adaptive step sizes for approximating a common solution of split equalities of equilibrium problem (EP), non-Lipschitz pseudomonotone variational inequality problem (VIP) and fixed point problem (FPP) of nonexpansive semigroups in real Hilbert spaces. We prove that the sequence generated by our proposed method converges strongly to a common solution of the EP, pseudomonotone VIP and FPP of nonexpansive semigroups without any linesearch procedure nor the sequential weak continuity condition often assumed by authors when solving non-Lipschitz VIPs. Finally, we provide some numerical experiments for the proposed method in comparison with related methods in the literature. Our result improves, extends and generalizes several of the existing results in this direction.

KW - Equilibrium problem

KW - Inertial technique

KW - Nonexpansive semigroup

KW - Self-adaptive step size

KW - Split equality problems

KW - Variational inequalities

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DO - 10.1007/s40306-023-00521-5

M3 - Article

AN - SCOPUS:85181969803

SN - 0251-4184

VL - 48

SP - 621

EP - 650

JO - Acta Mathematica Vietnamica

JF - Acta Mathematica Vietnamica

IS - 4

ER -

An inertial iterative algorithm for approximating common solutions to split equalities of some nonlinear optimization problems

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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