Strongly convergent inertial extragradient type methods for equilibrium problems

Abstract

This paper studies modified extragradient methods with inertial extrapolation step and self-adaptive step-sizes for solving equilibrium problems in real Hilbert spaces. Strong convergence results are obtained under the assumption that the bifunction is pseudomonotone and satisfies the Lipchitz-type condition. Our method of proof is of independent interest and different from the recent arguments used in related papers on strong convergence methods with inertial steps for equilibrium problems. Numerical implementations and comparisons are given to support the theoretical findings.

Keywords:

• Equilibrium problems
• extragradient-type methods
• inertial steps
• fixed points
• Hilbert spaces

2020 Mathematics Subject Classifications:

• 47H05
• 47H09
• 47J30
• 65K15

Disclosure statement

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

Additional information

Funding

The research was partially supported by the National Natural Science Foundation of China under Grant No. [1217011852].