A nonmonotonic explicit proximal-like method for solving equilibrium programming with convex constraints

Document Type : Original Article


1 Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage, Pathumthani 13180, Thailand.

2 Mathematics and Computing Science Program, Faculty of Science and Technology, Phetchabun Rajabhat University, Phetchabun 67000, Thailand.

3 Faculty of Science and Technology, Rajamangala University of Technology Phra Nakhon (RMUTP), 1381 Pracharat 1 Road, Wongsawang, Bang Sue, Bangkok 10800, Thailand.

4 School of Science, University of Phayao, Phayao, 56000, Thailand.



In this paper, we propose a new proximal-type method to solve equilibrium problems in a real Hilbert space. The new method is analogous to the famous two step extragradient method that is used to solve variational inequalities in the Hilbert spaces. The proposed iterative scheme uses a new non-monotone step size rule based on local bifunction information instead of any line search method. A strong convergence theorem for the proposed method is well-established by taking mild conditions on a bifunction. The applications of the main results to solve fixed point problems and variational inequalities are presented. Finally, we examined two test problems for computational experiments and demonstrated the validity and effectiveness of the proposed method.