Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

Rose Maluleka; Godwin Chidi Ugwunnadi; Maggie Aphane

doi:10.3934/math.20231539

Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

Rose Maluleka, Godwin Chidi Ugwunnadi^*, Maggie Aphane

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.

Original language	English
Pages (from-to)	30102-30119
Number of pages	18
Journal	AIMS Mathematics
Volume	8
Issue number	12
DOIs	https://doi.org/10.3934/math.20231539
Publication status	Published - 2023
Externally published	Yes

Keywords

demimetric mapping
fixed point
quasimonotone operator
strong convergence
variational inequality problem

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10.3934/math.20231539

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abstract = "In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.",

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author = "Rose Maluleka and Ugwunnadi, {Godwin Chidi} and Maggie Aphane",

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AB - In this paper, we introduce a new modified inertial Mann-type method that combines the subgradient extragradient method with the projection contraction method for solving quasimonotone variational inequality problems and fixed point problems in real Hilbert spaces. We establish strong convergence of the proposed method under some mild conditions without knowledge of the operator norm. Finally, we give numerical experiments to illustrate the efficiency of the method over the existing one in the literature.

KW - demimetric mapping

KW - fixed point

KW - quasimonotone operator

KW - strong convergence

KW - variational inequality problem

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ER -

Inertial subgradient extragradient with projection method for solving variational inequality and fixed point problems

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Keywords

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