A method with inertial extrapolation step for convex constrained monotone equations

Springer Science and Business Media LLC - Tập 2021 Số 1 - 2021
Abdulkarim Hassan Ibrahim1, Poom Kumam1, Auwal Bala Abubakar2, Jamilu Abubakar3
1KMUTTFixed 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, Bangkok, 10140, Thailand
2Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University Kano, Kano, Nigeria
3Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria

Tóm tắt

AbstractIn 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.

Từ khóa


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