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Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems

Inertial extragradient algorithms with non-monotonic step sizes for solving variational... In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Operator Theory Springer Journals

Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems

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Publisher
Springer Journals
Copyright
Copyright © Tusi Mathematical Research Group (TMRG) 2021
ISSN
2662-2009
eISSN
2538-225X
DOI
10.1007/s43036-021-00155-0
Publisher site
See Article on Publisher Site

Abstract

In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.

Journal

Advances in Operator TheorySpringer Journals

Published: Jul 19, 2021

Keywords: Variational inequality problem; Fixed point problem; Subgradient extragradient method; Tseng’s extragradient method; Inertial method; Strong convergence; 47H09; 47J20; 49J40; 65J15; 90C30

References