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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.

Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces

Wairojjana Nopparat, Pakkaranang Nuttapol, Pholasa Nattawut

Demonstratio Mathematica

2021

Vol. 54, nr 1

110--128

In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.