An inertial based forward–backward algorithm for monotone inclusion problems and split mixed equilibrium problems in Hilbert spaces

Advances in Difference Equations

article

Arfat, Yasir¹  Kumam, Poom¹  Ngiamsunthorn, Parinya Sa¹  Khan, Muhammad Aqeel Ahmad⁴ 

[1] 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);Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT);Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, COMSATS University Islamabad

关键词: Mixed split equilibrium problem;    Inertial method;    Inclusion problem;    Forward–backward algorithm;    Shrinking projection method;   

DOI  :  10.1186/s13662-020-02915-3

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Iterative algorithms are widely applied to solve convex optimization problems under a suitable set of constraints. In this paper, we develop an iterative algorithm whose architecture comprises a modified version of the forward-backward splitting algorithm and the hybrid shrinking projection algorithm. We provide theoretical results concerning weak and strong convergence of the proposed algorithm towards a common solution of the monotone inclusion problem and the split mixed equilibrium problem in Hilbert spaces. Moreover, numerical experiments compare favorably the efficiency of the proposed algorithm with the existing algorithms. As a consequence, our results improve various existing results in the current literature.

【 授权许可】

CC BY