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Article

A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities

by
Uzoamaka Azuka Ezeafulukwe
1,
Besheng George Akuchu
1,
Godwin Chidi Ugwunnadi
2,3,* and
Maggie Aphane
3
1
Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria
2
Department of Mathematics, University of Eswatini, Kwaluseni M201, Eswatini
3
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria 0204, South Africa
*
Author to whom correspondence should be addressed.
Mathematics 2024, 12(14), 2203; https://doi.org/10.3390/math12142203
Submission received: 14 May 2024 / Revised: 21 June 2024 / Accepted: 12 July 2024 / Published: 13 July 2024
(This article belongs to the Section E: Applied Mathematics)
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Abstract

In this work, we study a new line-search rule for solving the pseudomonotone variational inequality problem with non-Lipschitz mapping in real Hilbert spaces as well as provide a strong convergence analysis of the sequence generated by our suggested algorithm with double inertial extrapolation steps. In order to speed up the convergence of projection and contraction methods with inertial steps for solving variational inequalities, we propose a new approach that combines double inertial extrapolation steps, the modified Mann-type projection and contraction method, and the line-search rule, which is based on the golden ratio (5+1)/2. We demonstrate the efficiency, robustness, and stability of the suggested algorithm with numerical examples.
Keywords: golden rule; line-search rule; projection and contraction method; variational inequality problem; strong convergence; Hilbert spaces golden rule; line-search rule; projection and contraction method; variational inequality problem; strong convergence; Hilbert spaces

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MDPI and ACS Style

Ezeafulukwe, U.A.; Akuchu, B.G.; Ugwunnadi, G.C.; Aphane, M. A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities. Mathematics 2024, 12, 2203. https://doi.org/10.3390/math12142203

AMA Style

Ezeafulukwe UA, Akuchu BG, Ugwunnadi GC, Aphane M. A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities. Mathematics. 2024; 12(14):2203. https://doi.org/10.3390/math12142203

Chicago/Turabian Style

Ezeafulukwe, Uzoamaka Azuka, Besheng George Akuchu, Godwin Chidi Ugwunnadi, and Maggie Aphane. 2024. "A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities" Mathematics 12, no. 14: 2203. https://doi.org/10.3390/math12142203

APA Style

Ezeafulukwe, U. A., Akuchu, B. G., Ugwunnadi, G. C., & Aphane, M. (2024). A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities. Mathematics, 12(14), 2203. https://doi.org/10.3390/math12142203

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