Linear Convergence for Quasi-Variational Inequalities with Inertial Projection-Type Method. (30th March 2022)

• Record Type: Journal Article
• Authors: Shehu, Yekini
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 16(2021)
• Page Start: 1865
• Page End: 1879
• Publication Date: 2022-03-30
• Subjects: Hilbert spaces -- inertial extrapolation step -- quasi-variational inequalities -- strongly monotone; 47H05 -- 47J20 -- 47J25 -- 65K15 -- 90C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1950762
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong convergence analysis of the sequence of iterates generated by our proposed method to the unique solution of quasi-variational inequality under some mild assumptions. Later, we show that the sequence converges linearly to the unique solution in a special case of choice of parameters. Another contribution in this article is that the inertial factor in our proposed method is allowed to be equal to 1 unlike other previously proposed inertial projection-type method for solving quasi-variational inequalities in the literature where inertial factor is assumed to be bounded away from 1.