A method with inertial extrapolation step for convex constrained monotone equations

• Published in: Journal of inequalities and applications 2021-12, Vol.2021 (1), p.1-25, Article 189
• Main Authors: Ibrahim, Abdulkarim Hassan, Kumam, Poom, Abubakar, Auwal Bala, Abubakar, Jamilu
• Format: Article
• Language: English
• Subjects: Algorithms; Analysis; Applications of Mathematics; Convergence; Derivative-free method; Extrapolation; Inertial algorithm; Iterative algorithms; Iterative method; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinear equations; Projection method
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-021-02719-3

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.