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

Uzoamaka Azuka Ezeafulukwe, Besheng George Akuchu, Godwin Chidi Ugwunnadi () and Maggie Aphane
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Uzoamaka Azuka Ezeafulukwe: Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria
Besheng George Akuchu: Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria
Godwin Chidi Ugwunnadi: Department of Mathematics, University of Eswatini, Kwaluseni M201, Eswatini
Maggie Aphane: Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria 0204, South Africa

Mathematics, 2024, vol. 12, issue 14, 1-16

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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