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On solving pseudomonotone equilibrium problems via two new extragradient-type methods under convex constraints

Khunpanuk Chainarong, Pakkaranang Nuttapol, Pholasa Nattawut

Demonstratio Mathematica

2022

Vol. 55, nr 1

297--314

The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both new algorithms are analogous to the well-known two-step extragradient algorithm for solving the variational inequality problem in Hilbert spaces. The proposed iterative algorithms use a new step size rule based on local bifunction information instead of the line search technique. Two weak convergence theorems for both algorithms are well-established by letting mild conditions. The main results are used to solve the fixed point and variational inequality problems. Finally, we present several computational experiments to demonstrate the efficiency and effectiveness of the proposed algorithms.

Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications

Pakkaranang Nuttapol, Rehman Habib ur, Kumam Wiyada

Demonstratio Mathematica

2021

Vol. 54, nr 1

280--298

The aim of this paper is to propose two new modified extragradient methods to solve the pseudo-monotone equilibrium problem in a real Hilbert space with the Lipschitz-type condition. The iterative schemes use a new step size rule that is updated on each iteration based on the value of previous iterations. By using mild conditions on a bi-function, two strong convergence theorems are established. The applications of proposed results are studied to solve variational inequalities and fixed point problems in the setting of real Hilbert spaces. Many numerical experiments have been provided in order to show the algorithmic performance of the proposed methods and compare them with the existing ones.