TY - JOUR
T1 - PROJECTION METHOD WITH INERTIAL STEP FOR NONLINEAR EQUATIONS
T2 - APPLICATION TO SIGNAL RECOVERY
AU - Ibrahim, Abdulkarim Hassan
AU - Kumam, Poom
AU - Sun, Min
AU - Chaipunya, Parin
AU - Abubakar, Auwal Bala
N1 - Funding Information:
Acknowledgments. 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 PhD Research Scholarship from King Mongkut’s University of Technology Thon-buri (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 project is funded by National Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). The last author acknowledges with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Funding Information:
2020 Mathematics Subject Classification. Primary: 65F10, 90C52, 65K05. Key words and phrases. Iterative method, inertial algorithm, nonlinear equations, derivative-free method, projection method, signal recovery. The first author is supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi (Grant no. 16/2561). ∗ Corresponding author: Poom Kumam.
Publisher Copyright:
© 2022, Journal of Industrial and Management Optimization. All Rights Reserved.
PY - 2023/1
Y1 - 2023/1
N2 - In this paper, using the concept of inertial extrapolation, we introduce a globally convergent inertial extrapolation method for solving nonlinear equations with convex constraints for which the underlying mapping is monotone and Lipschitz continuous. The method can be viewed as a combination of the efficient three-term derivative-free method of Gao and He [Calcolo. 55(4), 1-17, 2018] with the inertial extrapolation step. Moreover, the algorithm is designed such that at every iteration, the method is free from derivative evaluations. Under standard assumptions, we establish the global convergence results for the proposed method. Numerical implementations illustrate the performance and advantage of this new method. Moreover, we also extend this method to solve the LASSO problems to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of our algorithm.
AB - In this paper, using the concept of inertial extrapolation, we introduce a globally convergent inertial extrapolation method for solving nonlinear equations with convex constraints for which the underlying mapping is monotone and Lipschitz continuous. The method can be viewed as a combination of the efficient three-term derivative-free method of Gao and He [Calcolo. 55(4), 1-17, 2018] with the inertial extrapolation step. Moreover, the algorithm is designed such that at every iteration, the method is free from derivative evaluations. Under standard assumptions, we establish the global convergence results for the proposed method. Numerical implementations illustrate the performance and advantage of this new method. Moreover, we also extend this method to solve the LASSO problems to decode a sparse signal in compressive sensing. Performance comparisons illustrate the effectiveness and competitiveness of our algorithm.
KW - Derivativefree method
KW - Inertial algorithm
KW - Iterative method
KW - Nonlinear equations
KW - Projection method
KW - Signal recovery.
UR - http://www.scopus.com/inward/record.url?scp=85138178492&partnerID=8YFLogxK
U2 - 10.3934/jimo.2021173
DO - 10.3934/jimo.2021173
M3 - Article
AN - SCOPUS:85138178492
SN - 1547-5816
VL - 19
SP - 30
EP - 55
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -