Extragradient methods with dual inertial steps for solving equilibrium problems

ABSTRACT

The primary focus of this study is how to expedite the convergence rate of the extragradient method by tactfully choosing inertial parameters and building up the step-size rule. To achieve this goal, we introduce three improvements to Korpelevich's extragradient method. These improvements include the use of dual inertial steps as well as a self-adaptive step-size rule. The proposed iterative techniques are employed for solving equilibrium problems in real Hilbert spaces. Initially, we establish the results for weak convergence of the proposed methods, assuming the involved bifunction to be both pseudomonotone and Lipschitz-type continuous. Subsequently, we demonstrate linear convergence in scenarios where the bifunction is strongly pseudomonotone and Lipschitz-type continuous. Finally, we present multiple numerical experiments to illustrate the practical effectiveness of the proposed methods.

KEYWORDS:

• Equilibrium problems
• extragradient method
• pseudomonotone bifunction
• strongly pseudomonotone bifunction
• strong convergence

AMS SUBJECT CLASSIFICATIONS:

• 65Y05
• 65K15
• 47H05
• 47H10

Acknowledgments

Authors are thankful to the reviewers for their valuable comments to improve the paper.

Disclosure statement

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

Author's contributions

All authors contributed equally and significantly to writing this article.

Additional information

Funding

Habib ur Rehman acknowledges the financial support provided by the Zhejiang Normal University, Jinhua, 321004, People's Republic of China. Debdas Ghosh is thankful for the research grants MATRICS (MTR/2021/000696) and Core Research Grant (CRG/2022/001347) by the Science and Engineering Research Board, India. Jen-Chih Yao acknowledges the funding MOST 111-2115-M-039-001-MY2, Taiwan.