An improved convex constrained conjugate gradient descent method for nonlinear monotone equations with signal recovery applications

Habibu Abdullahi; A. K. Awasthi; Mohammed Yusuf Waziri; Issam A. R. Moghrabi; Abubakar Sani Halilu; Kabiru Ahmed; Sulaiman M. Ibrahim; Yau Balarabe Musa; Elissa M. Nadia; Habibu Abdullahi; A. K. Awasthi; Mohammed Yusuf Waziri; Issam A. R. Moghrabi; Abubakar Sani Halilu; Kabiru Ahmed; Sulaiman M. Ibrahim; Yau Balarabe Musa; Elissa M. Nadia

doi:10.3934/math.2025365

AIMS Mathematics

2025, Volume 10, Issue 4: 7941-7969. doi: 10.3934/math.2025365

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An improved convex constrained conjugate gradient descent method for nonlinear monotone equations with signal recovery applications

1.
Department of Mathematics, Sule Lamido University Kafin Hausa, Nigeria
2.
Numerical Optimization Research Group, Bayero University Kano, Nigeria
3.
Department of Mathematics, Lovely Professional University, Phagwara, India
4.
Department of Mathematical Sciences, Bayero University, Kano, Nigeria
5.
Information Systems and Technology Department, Kuwait Technical College, Kuwait
6.
School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, 06010, Kedah, Malaysia
7.
Faculty of Education and Arts Sohar University, Sohar 311, Oman
8.
Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Campus Besut, 22200 Terengganu, Malaysia

Received: 19 October 2024 Revised: 20 February 2025 Accepted: 26 February 2025 Published: 07 April 2025
MSC : 65K0519, 90C06, 90C30, 90C47, 90C90

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.
- conjugate descent,
- eigenvalue analysis,
- convex constraints,
- compressive sensing,
- search direction matrix,
- positive definite matrix
Citation: Habibu Abdullahi, A. K. Awasthi, Mohammed Yusuf Waziri, Issam A. R. Moghrabi, Abubakar Sani Halilu, Kabiru Ahmed, Sulaiman M. Ibrahim, Yau Balarabe Musa, Elissa M. Nadia. An improved convex constrained conjugate gradient descent method for nonlinear monotone equations with signal recovery applications[J]. AIMS Mathematics, 2025, 10(4): 7941-7969. doi: 10.3934/math.2025365

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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.

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