Shrinking Accelerated Forward-Backward-Forward Method for Split Equilibrium Problem and Monotone Inclusion Problem in Hilbert Spaces

Authors

Keywords:

Monotone Inclusion Problem, Split Equilibrium Problem, Shrinking Projection Iterates, Forward-Backward-Forward Iterates

Abstract

We propose and analyze a hybrid splitting method, comprises of forward-backward-forward iterates, shrinking projection iterates and Nesterov’s acceleration method, to solve the monotone inclusion problem associated with maximal monotone operators and split equilibrium problem in Hilbert spaces. The proposed iterative method exhibits accelerated strong convergence characteristics under suitable set of control conditions in such framework. Finally, we explore some useful applications of the proposed iterative method via Numerical experiment.

Author Biographies

Yasir Arfat, King Mongkut’s University of Technology Thonburi (KMUTT)

PhD. in Mathematics at  KMUTT Fixed Point Research Laboratory, KMUTT-Fixed Point Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.

Kamonrat Sombut, Applied Mathematics for Science and Engineering Research Unit (AMSERU), Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT)

Lecturer in Mathematics at Rajamangala University of Technology Thanyaburi (RMUTT), Pathum Thani 12110, Thailand.

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Published

2022-06-03

How to Cite

Arfat, Y., & Sombut, K. (2022). Shrinking Accelerated Forward-Backward-Forward Method for Split Equilibrium Problem and Monotone Inclusion Problem in Hilbert Spaces. Nonlinear Convex Analysis and Optimization: An International Journal on Numerical, Computation and Applications, 1(1), 75–95. Retrieved from https://bangmodjmcs.com/index.php/ncao/article/view/78

Issue

Vol. 1 No. 1 (2022): January - June, 2022

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Articles

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Copyright (c) 2022 Yasir Arfat, Kamonrat Sombut

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