Iterative regularization methods for solving equilibrium problems

Abstract

The paper concerns with two new schemes for approximating solutions of equilibrium problems involving monotone and Lipschitz-type bifunctions in Hilbert spaces. We describe how to incorporate the two-step proximal-like method (modified extragradient method) with the regularization technique and then we propose two iterative regularization algorithms for solving equilibrium problems. Unlike the viscosity-like methods, we establish the strong convergence of the new algorithms based on the regularization. The first algorithm is designed to work with the prior knowledge of Lipschitz-type constants of bifunction while the second one, with a simple stepsize rule, is done without this requirement. In order to illustrate the effectiveness and the convergence of the algorithms, we provide several numerical experiments in comparisons with other well known algorithms, which show that our new algorithms are effective for solving equilibrium problems.wi

Keywords:

• Equilibrium problem
• regularization
• monotonicity
• Lipschitz-type condition
• extragradient method

2010 Mathematics Subject Classifications:

• 65K10
• 65K15
• 90C30
• 47H05

Acknowledgements

The authors would like to thank the editor and the anonymous referees who kindly reviewed the paper and provided their valuable comments and suggestions.

Disclosure statement

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

Additional information

Funding

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 101.01-2020.06].