TY - JOUR
T1 - A derivative-free projection method for nonlinear equations with non-Lipschitz operator
T2 - Application to LASSO problem
AU - Ibrahim, Abdulkarim Hassan
AU - Kumam, Poom
AU - Abubakar, Auwal Bala
AU - Abubakar, Jamilu
N1 - Funding Information:
We are grateful to the referee for the useful suggestions. The authors acknowledge (i) the financial support provided by the Centre of Excellence in Theoretical and Computational Science (TaCS‐CoE), KMUTT, and (ii) the financial support provided by “Mid‐Career Research Grant” (N41A640089). In addition, the first author was supported by King Mongkut's University of Technology Thonburi's Postdoctoral Fellowship. Also, the first and third author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Funding Information:
We are grateful to the referee for the useful suggestions. The authors acknowledge (i) the financial support provided by the Centre of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT, and (ii) the financial support provided by “Mid-Career Research Grant” (N41A640089). In addition, the first author was supported by King Mongkut's University of Technology Thonburi's Postdoctoral Fellowship. Also, the first and third author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Publisher Copyright:
© 2023 John Wiley & Sons, Ltd.
PY - 2023
Y1 - 2023
N2 - In this paper, we introduce a derivative-free iterative method for finding the solutions of convex constrained nonlinear equations (CCNE) using the projection strategy. The new approach is free from gradient evaluations at each iteration. Also, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Compared with traditional methods for solving CCNE that assumes Lipschitz continuity and monotonicity to establish the global convergence result, an advantage of our proposed method is that the global convergence result does not require the assumption of Lipschitz continuity. Moreover, the underlying operator is assumed to be pseudomonotone, which is a milder condition than monotonicity. As an applications, we solve the LASSO problem in compressed sensing. Numerical experiments illustrate the performances of our proposed algorithm and provide a comparison with related algorithms.
AB - In this paper, we introduce a derivative-free iterative method for finding the solutions of convex constrained nonlinear equations (CCNE) using the projection strategy. The new approach is free from gradient evaluations at each iteration. Also, the search direction generated by the proposed method satisfies the sufficient descent property, which is independent of the line search. Compared with traditional methods for solving CCNE that assumes Lipschitz continuity and monotonicity to establish the global convergence result, an advantage of our proposed method is that the global convergence result does not require the assumption of Lipschitz continuity. Moreover, the underlying operator is assumed to be pseudomonotone, which is a milder condition than monotonicity. As an applications, we solve the LASSO problem in compressed sensing. Numerical experiments illustrate the performances of our proposed algorithm and provide a comparison with related algorithms.
KW - derivative-free method
KW - iterative method
KW - nonlinear equations
KW - projection method
KW - pseudomonotone operator
UR - http://www.scopus.com/inward/record.url?scp=85147223274&partnerID=8YFLogxK
U2 - 10.1002/mma.9033
DO - 10.1002/mma.9033
M3 - Article
AN - SCOPUS:85147223274
SN - 0170-4214
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
ER -