Convergence Analysis of Self-Adaptive Inertial Extra-Gradient Method for Solving a Family of Pseudomonotone Equilibrium Problems with Application

Abstract

In this article, we propose a new modified extragradient-like method to solve pseudomonotone equilibrium problems in real Hilbert space with a Lipschitz-type condition on a bifunction. This method uses a variable stepsize formula that is updated at each iteration based on the previous iterations. The advantage of the method is that it operates without prior knowledge of Lipschitz-type constants and any line search method. The weak convergence of the method is established by taking mild conditions on a bifunction. In the context of an application, fixed-point theorems involving strict pseudo-contraction and results for pseudomonotone variational inequalities are considered. Many numerical results have been reported to explain the numerical behavior of the proposed method.

A Parallel Hybrid Bregman Subgradient Extragradient Method for a System of Pseudomonotone Equilibrium and Fixed Point Problems

“…Some numerical examples are presented to show the efficiency and accuracy of the proposed method. This result improves and extends the results of [17][18][19][20]22,25,47,[49][50][51] and many other results in the literature.…”

“…Meanwhile, in Algorithm 1, the stepsize is chosen self-adaptively and does not require the prior estimates of the Lipschitz-like constant of the finite bifunctions. (iii) Furthermore, when E is the real Hilbert space, our Algorithm 1 improves the algorithms of [18,[47][48][49][50] in the setting of real Hilbert spaces. (iv) Furthermore, when E is a real Hilbert space and N = 1, M = 1, our Algorithm 1 improves and compliments the algorithms of [17,20,22,24,25,51].…”

“…Furthermore, when E is a real Hilbert space, our Algorithm 1 becomes the following algorithm, which improves the algorithm in [18,50], and the references therein.…”