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Inertial Extra-Gradient Method for Solving a Family of Strongly Pseudomonotone Equilibrium Problems in Real Hilbert Spaces with Application in Variational Inequality Problem
 
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Symmetry
Volume 12
Issue 4
10.3390/sym12040523
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Article

A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems

by
Habib ur Rehman
1,†,
Poom Kumam
1,2,3,*,†,
Ioannis K. Argyros
4,†,
Nasser Aedh Alreshidi
5,†,
Wiyada Kumam
6,*,† and
Wachirapong Jirakitpuwapat
1,†
1
KMUTTFixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, SCL 802 Fixed Point Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2
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
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
5
Department of Mathematics, College of Science, Northern Border University, Arar 73222, Saudi Arabia
6
Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi, Pathumthani 12110, Thailand
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Symmetry 2020, 12(4), 523; https://doi.org/10.3390/sym12040523
Received: 19 February 2020 / Revised: 8 March 2020 / Accepted: 24 March 2020 / Published: 2 April 2020
(This article belongs to the Special Issue Iterative Numerical Functional Analysis with Applications)
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Abstract

The main objective of this article is to propose a new method that would extend Popov’s extragradient method by changing two natural projections with two convex optimization problems. We also show the weak convergence of our designed method by taking mild assumptions on a cost bifunction. The method is evaluating only one value of the bifunction per iteration and it is uses an explicit formula for identifying the appropriate stepsize parameter for each iteration. The variable stepsize is going to be effective for enhancing iterative algorithm performance. The variable stepsize is updating for each iteration based on the previous iterations. After numerical examples, we conclude that the effect of the inertial term and variable stepsize has a significant improvement over the processing time and number of iterations. View Full-Text
Keywords: subgradient extragradient method; equilibrium problem; pseudomonotone equilibrium problems; lipschitz-type conditions; weak convergence; variational inequality problems subgradient extragradient method; equilibrium problem; pseudomonotone equilibrium problems; lipschitz-type conditions; weak convergence; variational inequality problems
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MDPI and ACS Style

Rehman, H.u.; Kumam, P.; Argyros, I.K.; Alreshidi, N.A.; Kumam, W.; Jirakitpuwapat, W. A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems. Symmetry 2020, 12, 523. https://doi.org/10.3390/sym12040523

AMA Style

Rehman Hu, Kumam P, Argyros IK, Alreshidi NA, Kumam W, Jirakitpuwapat W. A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems. Symmetry. 2020; 12(4):523. https://doi.org/10.3390/sym12040523

Chicago/Turabian Style

Rehman, Habib u., Poom Kumam, Ioannis K. Argyros, Nasser A. Alreshidi, Wiyada Kumam, and Wachirapong Jirakitpuwapat. 2020. "A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems" Symmetry 12, no. 4: 523. https://doi.org/10.3390/sym12040523

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