A method with inertial extrapolation step for convex constrained monotone equations

Journal of Inequalities and Applications

Auwal Bala Abubakar¹  Jamilu Abubakar²  Abdulkarim Hassan Ibrahim³  Poom Kumam⁴ 

[1] Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano, Kano, Nigeria;Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, 0204, Pretoria, Medunsa, South Africa;Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria;KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;

关键词: Iterative method;    Inertial algorithm;    Nonlinear equations;    Derivative-free method;    Projection method;   

DOI  :  10.1186/s13660-021-02719-3

来源: Springer

【 摘 要 】

In recent times, various algorithms have been incorporated with the inertial extrapolation step to speed up the convergence of the sequence generated by these algorithms. As far as we know, very few results exist regarding algorithms of the inertial derivative-free projection method for solving convex constrained monotone nonlinear equations. In this article, the convergence analysis of a derivative-free iterative algorithm (Liu and Feng in Numer. Algorithms 82(1):245–262, 2019) with an inertial extrapolation step for solving large scale convex constrained monotone nonlinear equations is studied. The proposed method generates a sufficient descent direction at each iteration. Under some mild assumptions, the global convergence of the sequence generated by the proposed method is established. Furthermore, some experimental results are presented to support the theoretical analysis of the proposed method.

【 授权许可】

CC BY