TY - JOUR
T1 - A hybrid approach for finding approximate solutions to constrained nonlinear monotone operator equations with applications
AU - Abubakar, Auwal Bala
AU - Kumam, Poom
AU - Mohammad, Hassan
AU - Ibrahim, Abdulkarim Hassan
AU - Kiri, Aliyu Ibrahim
N1 - Funding Information:
The authors thank the referees for their corrections and suggestions which improved the earlier version of this manuscript. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut's University of Technology Thonburi (KMUTT), Thailand. Moreover, this project is funded by National Research Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089). Also, the first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University.
Funding Information:
The authors thank the referees for their corrections and suggestions which improved the earlier version of this manuscript. The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT . Also, the (first) author, (Dr. Auwal Bala Abubakar) would like to thank the Postdoctoral Fellowship from King Mongkut's University of Technology Thonburi (KMUTT), Thailand. Moreover, this project is funded by National Research Council of Thailand (NRCT) under Research Grants for Talented Mid-Career Researchers (Contract no. N41A640089 ). Also, the first author acknowledge with thanks, the Department of Mathematics and Applied Mathematics at the Sefako Makgatho Health Sciences University .
Publisher Copyright:
© 2022 IMACS
PY - 2022/7
Y1 - 2022/7
N2 - In this article, a hybrid approach technique incorporated with three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is defined such that it is close to the one obtained by the memoryless Broyden-Fletcher-Goldferb-Shanno (BFGS) method. Independent of the line search, the search direction possesses the sufficient descent and trust region properties. Furthermore, the sequence of iterates generated converge globally under some appropriate assumptions. In addition, numerical experiments are carried out to test the efficiency of the proposed method in contrast with existing methods. Finally, the applicability of the proposed method in compressive sensing is shown.
AB - In this article, a hybrid approach technique incorporated with three-term conjugate gradient (CG) method is proposed to solve constrained nonlinear monotone operator equations. The search direction is defined such that it is close to the one obtained by the memoryless Broyden-Fletcher-Goldferb-Shanno (BFGS) method. Independent of the line search, the search direction possesses the sufficient descent and trust region properties. Furthermore, the sequence of iterates generated converge globally under some appropriate assumptions. In addition, numerical experiments are carried out to test the efficiency of the proposed method in contrast with existing methods. Finally, the applicability of the proposed method in compressive sensing is shown.
KW - Compressed sensing
KW - Derivative-free projection method
KW - Global convergence
KW - Monotone operator equations
UR - http://www.scopus.com/inward/record.url?scp=85126570286&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2022.03.001
DO - 10.1016/j.apnum.2022.03.001
M3 - Article
AN - SCOPUS:85126570286
SN - 0168-9274
VL - 177
SP - 79
EP - 92
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -