TY - JOUR
T1 - A Derivative-Free MZPRP Projection Method for Convex Constrained Nonlinear Equations and Its Application in Compressive Sensing
AU - Sulaiman, Ibrahim Mohammed
AU - Awwal, Aliyu Muhammed
AU - Malik, Maulana
AU - Pakkaranang, Nuttapol
AU - Panyanak, Bancha
N1 - Funding Information:
The fourth author was partially funded by Phetchabun Rajabhat University. The fifth author was supported by Chiang Mai University and the NSRF via the Program Management Unit for Human Resources and Institutional Development, Research and Innovation (grant number B05F640183).
Publisher Copyright:
© 2022 by the authors.
PY - 2022/8
Y1 - 2022/8
N2 - Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conjugate gradient method, in such a way that it is sufficiently descent. It is worth noting that, unlike many existing methods that require a monotonicity assumption to prove the convergence result, our new method needs the underlying function to be pseudomonotone, which is a weaker assumption. The performance of the proposed algorithm is demonstrated on a set of some test problems and applications arising from compressive sensing. The obtained results confirm that the proposed method is effective compared to some existing algorithms in the literature.
AB - Nonlinear systems of equations are widely used in science and engineering and, therefore, exploring efficient ways to solve them is paramount. In this paper, a new derivative-free approach for solving a nonlinear system of equations with convex constraints is proposed. The search direction of the proposed method is derived based on a modified conjugate gradient method, in such a way that it is sufficiently descent. It is worth noting that, unlike many existing methods that require a monotonicity assumption to prove the convergence result, our new method needs the underlying function to be pseudomonotone, which is a weaker assumption. The performance of the proposed algorithm is demonstrated on a set of some test problems and applications arising from compressive sensing. The obtained results confirm that the proposed method is effective compared to some existing algorithms in the literature.
KW - compressive sensing
KW - global convergence
KW - nonlinear problems
KW - numerical algorithms
KW - projection method
KW - pseudomonotone function
UR - http://www.scopus.com/inward/record.url?scp=85137389333&partnerID=8YFLogxK
U2 - 10.3390/math10162884
DO - 10.3390/math10162884
M3 - Article
AN - SCOPUS:85137389333
VL - 10
JO - Mathematics
JF - Mathematics
SN - 2227-7390
IS - 16
M1 - 2884
ER -