Viscosity-regularization iterative methods for solving equilibrium problems in Hilbert space

Abstract

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods.

Keywords:

• Equilibrium problem
• iterative method
• lipschitz-type condition
• monotonicity

AMS Subject Classifications:

• 65Y05
• 65K15

Disclosure statement

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

Additional information

Funding

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions on the original version of this paper. Simeon Reich was partially supported by the Israel Science Foundation [grant number 820/17], the Fund for the Promotion of Research at the Technion and by the Technion General Research Fund.