The inertial iterative extragradient methods for solving pseudomonotone equilibrium programming in Hilbert spaces

Journal of Inequalities and Applications

Wiyada Kumam¹  Poom Kumam²  Habib ur Rehman²  Ioannis K. Argyros³  Meshal Shutaywi⁴ 

[1] Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT);Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Mathematical Sciences, Cameron University;Department of Mathematics, College of Science & Arts, King Abdulaziz University;

关键词: Equilibrium problem;    Iterative method;    Pseudomonotone bifunction;    Weak convergence theorem;   

DOI  :  10.1186/s13660-022-02790-4

来源: DOAJ

【 摘 要 】

Abstract In this paper, we present new iterative techniques for approximating the solution of an equilibrium problem involving a pseudomonotone and a Lipschitz-type bifunction in Hilbert spaces. These techniques consist of two computing steps of a proximal-type mapping with an inertial term. Improved simplified stepsize rules that do not involve line search are investigated, allowing the method to be implemented more quickly without knowing the Lipschitz-type constants of a bifunction. The iterative sequences converge weakly on a specific solution to the problem when the control parameter conditions are properly specified. The numerical tests were carried out, and the results demonstrated the applicability and quick convergence of innovative approaches over earlier ones.

【 授权许可】

Unknown