Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
---|---|---|
Page(s) | 2561 - 2584 | |
DOI | https://doi.org/10.1051/ro/2023099 | |
Published online | 10 October 2023 |
Global convergence via modified self-adaptive approach for solving constrained monotone nonlinear equations with application to signal recovery problems
1
School of Mathematics and Statistics, HNP-LAMA, Central South University, Changsha, Hunan 410083, P.R. China
2
Department of Mathematics, Faculty of Natural and Applied Sciences, Sule Lamido University, Kafin-Hausa, Nigeria
3
Numerical Optimization Research Group, Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, Kano, Kano, Nigeria
4
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, Pretoria, Medunsa 0204, South Africa
5
Department of Mathematics, School of Science, Jigawa State College of Education, Gumel, Nigeria
* Corresponding author: muhammad.abdullahi@slu.edu.ng
Received:
13
August
2022
Accepted:
4
July
2023
The conjugate gradient method (CG) is one of the most rapidly expanding and efficient ways of solving unconstrained minimization problems. Recently, there has been a lot of effort put into extending the CG approach to solve monotone nonlinear equations. In this paper, we describe a variation of the CG method for solving constrained monotone nonlinear equations. The approach has a sufficient descent property, and its global convergence has been demonstrated with the help of some reasonable assumptions. Two sets of numerical tests were run to demonstrate the proposed method’s superior performance when compared to other methods. The initial experiment aimed to solve nonlinear equations with constraints, while in the second experiment, the method was applied to sparse signal reconstruction.
Mathematics Subject Classification: 65K05 / 90C52 / 90C56 / 94A08
Key words: Non-linear equations / signal processing / projection map / convex constraint / global convergence
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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