Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A NEW EXPLICIT EXTRAGRADIENT METHOD FOR SOLVING EQUILIBRIUM PROBLEMS WITH CONVEX CONSTRAINTS

  • Muangchoo, Kanikar (Faculty of Science and Technology Rajamangala University of Technology Phra Nakhon (RMUTP))
  • Received : 2020.12.04
  • Accepted : 2021.09.06
  • Published : 2022.03.15
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Abstract

The purpose of this research is to formulate a new proximal-type algorithm to solve the equilibrium problem in a real Hilbert space. A new algorithm is analogous to the famous two-step extragradient algorithm that was used to solve variational inequalities in the Hilbert spaces previously. The proposed iterative scheme uses a new step size rule based on local bifunction details instead of Lipschitz constants or any line search scheme. The strong convergence theorem for the proposed algorithm is well-proven by letting mild assumptions about the bifunction. Applications of these results are presented to solve the fixed point problems and the variational inequality problems. Finally, we discuss two test problems and computational performance is explicating to show the efficiency and effectiveness of the proposed algorithm.

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Acknowledgement

This project was supported by Rajamangala University of Technology Phra Nakhon (RMUTP).

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