@article{Abdullahi2025, 
author = {Habibu Abdullahi and A. K. Awasthi and Mohammed Yusuf Waziri and Issam A. R. Moghrabi and Abubakar Sani Halilu and Kabiru Ahmed and Sulaiman M. Ibrahim and Yau Balarabe Musa and Elissa M. Nadia},
title = {An improved convex constrained conjugate gradient descent method for nonlinear monotone equations with signal recovery applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {4},
pages = {7941-7969},
keywords = {conjugate descent, eigenvalue analysis, convex constraints, compressive sensing, search direction matrix, positive definite matrix},
url = {https://www.sciopen.com/article/10.3934/math.2025365},
doi = {10.3934/math.2025365},
abstract = {The conjugate descent (CD) method is a conjugate gradient (CG) variant with remarkable convergence properties. This paper presents a modified CD scheme for solving systems of constrained monotone nonlinear equations. Eigenvalue analysis demonstrates that the proposed search direction matrix is positive definite. By incorporating the proposed algorithm with Solodov and Svaiter's projection method (1999), several convex-constrained monotone nonlinear equations were solved, yielding impressive results. The new algorithm exhibits descent properties and achieves global convergence under appropriate assumptions. Numerical comparisons with recent algorithms in the literature highlight the efficiency and effectiveness of the proposed method. Furthermore, the method is applied to signal recovery experiments in compressive sensing.}
}