New three-term conjugate gradient algorithm for solving monotone nonlinear equations and signal recovery problems

Abstract

This work presents a new three-term projection algorithm for solving nonlinear monotone equations. The paper is aimed at constructing an efficient and competitive algorithm for finding approximate solutions of nonlinear monotone equations. This is based on a new choice of the conjugate gradient direction which satisfies the sufficient descent condition. The convergence of the algorithm is shown under Lipschitz continuity and monotonicity of the involved operator. Numerical experiments presented in the paper show that the algorithm needs a less number of iterations in comparison with existing algorithms. Furthermore, the proposed algorithm is applied to solve signal recovery problems.

Keywords:

• Nonlinear equations
• conjugate gradient
• projection map
• signal recovery

Mathematics Subject Classifications:

• 65K05
• 90C52
• 90C56
• 94A08

Acknowledgments

This research work was completed during my visit to the Faculty of Natural Sciences II, Institute for Mathematics, Martin Luther University Halle-Wittenberg, 06099 Halle (Saale), Germany We thank Peiting Gao affiliate at Chongqing University for providing us with access to Algorithm 4.1 MATLAB codes for signal recovery. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut's University of Technology Thonburi (KMUTT), Thailand. The first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This project was supported by Petchra Pra Jom Klao Doctoral Academic Scholarship for Ph.D. Program at KMUTT. Moreover, this project was partially supported by the the National Research Council of Thailand (NRCT) under project ‘Mid-Career Research Grant’ [N41A640089].