INERTIAL MANN-TYPE ITERATIVE METHOD FOR SOLVING SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

Jacob Ashiwere Abuchu; Godwin Chidi Ugwunnadi; Ojen Kumar Narain

doi:10.3934/jimo.2022075

INERTIAL MANN-TYPE ITERATIVE METHOD FOR SOLVING SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

Jacob Ashiwere Abuchu^*, Godwin Chidi Ugwunnadi, Ojen Kumar Narain

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

In this paper, we study a modiffed relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As applications, some special cases of the general problem are given. Finally, we also give some numerical illustrations of the proposed method in comparison with other methods in the literature to show the applicability and advantage of our results.

Original language	English
Pages (from-to)	3020-3043
Number of pages	24
Journal	Journal of Industrial and Management Optimization
Volume	19
Issue number	4
DOIs	https://doi.org/10.3934/jimo.2022075
Publication status	Published - Apr 2023
Externally published	Yes

Keywords

Split monotone variational inclusion problem
average operator
inertial iterative method
inverse strongly monotone
nonexpansive operator
strong convergence

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10.3934/jimo.2022075

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title = "INERTIAL MANN-TYPE ITERATIVE METHOD FOR SOLVING SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS",

abstract = "In this paper, we study a modiffed relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As applications, some special cases of the general problem are given. Finally, we also give some numerical illustrations of the proposed method in comparison with other methods in the literature to show the applicability and advantage of our results.",

keywords = "Split monotone variational inclusion problem, average operator, inertial iterative method, inverse strongly monotone, nonexpansive operator, strong convergence",

author = "Abuchu, {Jacob Ashiwere} and Ugwunnadi, {Godwin Chidi} and Narain, {Ojen Kumar}",

year = "2023",

month = apr,

doi = "10.3934/jimo.2022075",

language = "English",

volume = "19",

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journal = "Journal of Industrial and Management Optimization",

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AU - Abuchu, Jacob Ashiwere

AU - Ugwunnadi, Godwin Chidi

AU - Narain, Ojen Kumar

PY - 2023/4

Y1 - 2023/4

N2 - In this paper, we study a modiffed relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As applications, some special cases of the general problem are given. Finally, we also give some numerical illustrations of the proposed method in comparison with other methods in the literature to show the applicability and advantage of our results.

AB - In this paper, we study a modiffed relaxed inertial Mann-type iterative algorithm for solving split monotone variational inclusion problem without prior knowledge of the bounded linear operator norm in real Hilbert spaces. Under some appropriate assumptions on the parameters, we established a strong convergence result of the proposed algorithm. As applications, some special cases of the general problem are given. Finally, we also give some numerical illustrations of the proposed method in comparison with other methods in the literature to show the applicability and advantage of our results.

KW - Split monotone variational inclusion problem

KW - average operator

KW - inertial iterative method

KW - inverse strongly monotone

KW - nonexpansive operator

KW - strong convergence

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SP - 3020

EP - 3043

JO - Journal of Industrial and Management Optimization

JF - Journal of Industrial and Management Optimization

IS - 4

ER -

INERTIAL MANN-TYPE ITERATIVE METHOD FOR SOLVING SPLIT MONOTONE VARIATIONAL INCLUSION PROBLEM WITH APPLICATIONS

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Keywords

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