An inertial extragradient method for iteratively solving equilibrium problems in real Hilbert spaces

Abstract

In this article, we present an inertial subgradient extragradient-type method that uses a non-monotone step size rule to find a numerical solution to equilibrium problems in real Hilbert spaces. The presented iterative scheme is based on an extragradient subgradient method and an inertial-type scheme. In fact, the proposed iterative scheme is effective in terms of performance, and the key advantage derives directly from the use of the variable step size rule, which is revised by each iteration on the basis of the Lipschitz-type constants as well as certain prior iterations. We obtain a weak convergence theorem for a new method by using mild conditions on a bifunction. Applications of the main results are given to solve various nonlinear problems. Several numerical findings are given in order to illustrate the numerical behaviour of the proposed method and to compare it to others.

Keywords:

• Equilibrium problem
• Weak convergence theorem
• Lipschitz-type conditions
• Fixed point
• Hilbert space

2010 AMS Subject Classifications:

• 47H06
• 47H09
• 47J05
• 47J25

Acknowledgement

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.

Disclosure statement

No potential conflict of interest was reported by the author(s).