Next Article in Journal
Nonlocal Integro-Differential Equations of the Second Order with Degeneration
Next Article in Special Issue
Complex Intuitionistic Fuzzy Soft Lattice Ordered Group and Its Weighted Distance Measures
Previous Article in Journal
Convergence Rate of the Modified Landweber Method for Solving Inverse Potential Problems
Previous Article in Special Issue
Robust Dissipativity Analysis of Hopfield-Type Complex-Valued Neural Networks with Time-Varying Delays and Linear Fractional Uncertainties
Open AccessArticle

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

1
Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
2
Department of Mathematics, Usmanu Danfodiyo University, Sokoto 840001, Nigeria
3
Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Current address: Department of Mathematics, King Mongkut’s University of Technology Thonburi, 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
Mathematics 2020, 8(4), 609; https://doi.org/10.3390/math8040609
Received: 18 March 2020 / Revised: 6 April 2020 / Accepted: 8 April 2020 / Published: 16 April 2020
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. View Full-Text
Keywords: variational inequality problem; Lipschitz-type conditions; viscosity method; subgradient extragradient method; pseudomonotone operator variational inequality problem; Lipschitz-type conditions; viscosity method; subgradient extragradient method; pseudomonotone operator
Show Figures

Figure 1

MDPI and ACS Style

Abubakar, J.; Kumam, P.; Rehman, H.; Hassan Ibrahim, A. Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator. Mathematics 2020, 8, 609.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop