TY - JOUR
T1 - A method with inertial extrapolation step for convex constrained monotone equations
AU - Ibrahim, Abdulkarim Hassan
AU - Kumam, Poom
AU - Abubakar, Auwal Bala
AU - Abubakar, Jamilu
N1 - Funding Information:
We are grateful to the anonymous referees for their useful comments which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the “Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi” (Grant no. 16/2561). The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The third author acknowledges with thanks the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Funding Information:
We are grateful to the anonymous referees for their useful comments which have made the paper clearer and more comprehensive than the earlier version. The first author was supported by the “Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi” (Grant no. 16/2561). The authors also acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The third author acknowledges with thanks the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Derivative-free method
KW - Inertial algorithm
KW - Iterative method
KW - Nonlinear equations
KW - Projection method
UR - http://www.scopus.com/inward/record.url?scp=85120776533&partnerID=8YFLogxK
U2 - 10.1186/s13660-021-02719-3
DO - 10.1186/s13660-021-02719-3
M3 - Article
AN - SCOPUS:85120776533
SN - 1025-5834
VL - 2021
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
IS - 1
M1 - 189
ER -