Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator

Jamilu Abubakar, Poom Kumam, Habib ur Rehman and Abdulkarim Hassan Ibrahim
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Jamilu Abubakar: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Poom Kumam: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Habib ur Rehman: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Abdulkarim Hassan Ibrahim: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

Mathematics, 2020, vol. 8, issue 4, 1-25

Abstract: Two inertial subgradient extragradient algorithms for solving variational inequality problems involving pseudomonotone operator are proposed in this article. The iterative schemes use self-adaptive step sizes which do not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we show the weak and strong convergence of the sequences generated by the proposed algorithms. The strong convergence in the second algorithm follows from the use of viscosity method. Numerical experiments both in finite- and infinite-dimensional spaces are reported to illustrate the inertial effect and the computational performance of the proposed algorithms in comparison with the existing state of the art algorithms.

Keywords: variational inequality problem; Lipschitz-type conditions; viscosity method; subgradient extragradient method; pseudomonotone operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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